doi: 10.3934/dcdss.2022064
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications

1. 

School of Mathematics, Southeast University, Nanjing 210096, China

2. 

College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China

3. 

School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China

4. 

School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

* Corresponding author: Jinling Liang

Received  October 2021 Revised  January 2022 Early access March 2022

In this paper, the $ H_{\infty} $ control problem is concerned for a class of continuous-discrete T-S fuzzy systems (TSFSs) described by the Roesser model with a finite frequency (FF) specification. Assume that the frequencies of the disturbance input are known in advance and dominated within a FF range. An $ H_{\infty} $ performance is established within a FF range for continuous-discrete TSFSs, which is an extension of the standard $ H_{\infty} $ performance. This paper aims to construct a state feedback controller which guarantees the closed-loop system to be stable and to have a prescribed FF $ H_{\infty} $ performance. A numerical tractable method for designing a controller is obtained through matrixing, thus giving conveniently the expression of controller with linear matrix inequality as tool kit.

Citation: Zhaoxia Duan, Jinling Liang, Zhengrong Xiang. $ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022064
References:
[1]

S. E. BentonE. Rogers and D. H. Owens, Stability conditions for a class of 2D continuous-discrete linear systems with dynamic boundary conditions, Int. J. Control, 75 (2002), 52-60.  doi: 10.1080/00207170110086962.

[2]

J. Chen and R. J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Dordrecht, 1999. doi: 10.1007/978-1-4615-5149-2.

[3]

Y. ChenW. Zhang and H. Gao, Finite frequency $H_{\infty}$ control for building under earthquake excitation, Mechatronics, 20 (2010), 128-142. 

[4]

G. Chesi and R. H. Middleton, Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty, Automatica J. IFAC, 67 (2016), 233-243.  doi: 10.1016/j.automatica.2016.01.042.

[5]

G. Chesi and R. H. Middleton, Necessary and sufficient LMI conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems, IEEE Trans. Autom. Control, 59 (2014), 996-1007.  doi: 10.1109/TAC.2014.2299353.

[6]

D. DingQ.-L. HanZ. Wang and X. Ge, A survey on model-based distributed control and filtering for industrial cyber-physical systems, IEEE Trans. Ind. Inform., 15 (2019), 2483-2499.  doi: 10.1109/TII.2019.2905295.

[7]

D.-W. Ding and G.-H. Yang, Fuzzy filter design for nonlinear systems in finite-frequency domain, IEEE Trans. Fuzzy Syst., 18 (2010), 935-945.  doi: 10.1109/TFUZZ.2010.2058807.

[8]

C. DuL. XieG. Guo and J. N. Teoh, A generalized KYP lemma based approach for disturbance rejection in data storage systems, Automatica J. IFAC, 43 (2007), 2112-2118.  doi: 10.1016/j.automatica.2007.04.023.

[9]

Z. DuanI. Ghous and J. Shen, Fault detection observer design for discrete-time 2-D T-S fuzzy systems with finite-frequency specifications, Fuzzy Set. Syst., 392 (2020), 24-45.  doi: 10.1016/j.fss.2019.05.004.

[10]

G. Feng, Analysis and Synthesis of Fuzzy Control Systems: A Modeled-Based Approach, Taylor & Francis Group, Boca Raton, 2010.

[11]

E. Fornasini and G. Marchesini, State-space realization theory of two-dimensional filters, IEEE Trans. Autom. Control, AC-21 (1976), 484-492.  doi: 10.1109/tac.1976.1101305.

[12]

D. Franke, 2D-Analysis of Hybrid Systems, Advances in Control, Springer, London, (1999), 293–299.

[13]

T. Iwasaki and S. Hara, Generalized KYP lemma: Unified frequency domain inequalities with design applications, IEEE Trans. Autom. Control, 50 (2005), 41-59.  doi: 10.1109/TAC.2004.840475.

[14]

T. IwasakiS. Hara and A. L. Fradkov, Time domain interpretations of frequency domain inequalities on (semi)finite ranges, Syst. Control Lett., 54 (2005), 681-691.  doi: 10.1016/j.sysconle.2004.11.007.

[15]

T. Kaczorek, Two-Dimensional Linear Systems, Lecture Notes in Control and Information Sciences, 68. Springer-Verlag Berlin, Heidelberg, 1985.

[16]

S. H. Kim and P. Park, $H_{\infty}$ state-feedback-control design for discrete-time fuzzy systems using relaxation technique for parameterized LMI, IEEE Trans. Fuzzy Syst., 18 (2010), 985-993. 

[17]

S. Knorn, A Two-Dimensional Systems Stability Analysis of Vehicle Platoons, PhD Thesis, National University of Ireland Maynooth, 2013.

[18]

S. Knorn and R. H. Middleton, Asymptotic and exponential stability of nonlinear two-dimensional continuous-discrete Roesser models, Syst. Control Lett., 93 (2016), 35-42.  doi: 10.1016/j.sysconle.2016.03.004.

[19]

S. Knorn and R. H. Middleton, Stability of two-dimensional linear systems with singularities on the stability boundary using LMIs, IEEE Trans. Autom. Control, 58 (2013), 2579-2590.  doi: 10.1109/TAC.2013.2264852.

[20]

D. LiJ. Liang and F. Wang, Robust $H_{\infty}$ filtering for 2D systems with RON under the stochastic communication protocol, IET Control Theory Appl., 14 (2020), 2795-2804. 

[21]

L. LiS. X. DingJ. QiuY. Yang and D. Xu, Fuzzy observer-based fault detection design approach for nonlinear processes, IEEE Trams. Syst., Man., Cybern., Syst., 47 (2017), 1941-1952. 

[22]

L. Li and W. Wang, Fuzzy modeling and $H_{\infty}$ control for general 2D nonlinear systems, Fuzzy Set. Syst., 207 (2012), 1-26.  doi: 10.1016/j.fss.2012.04.002.

[23]

J. LiangJ. Wang and T. Huang, $l_1$ filtering for continuous-discrete T-S fuzzy positive Roesser model, J. Franklin Inst., 355 (2018), 7281-7305.  doi: 10.1016/j.jfranklin.2018.07.017.

[24]

X. LiangJ. XiaG. ChenH. Zhang and Z. Wang, $H_{\infty}$ control for fuzzy Markovian jump systems based on sampled-data control method, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1329-1343.  doi: 10.3934/dcdss.2020368.

[25]

S. LiuL. ZhaoW. ZhangX. Yang and F. E. Alsaadi, Fast fixed-time synchronization of T-S fuzzy complex networks, Nonlinear Anal. Model. Control, 26 (2021), 597-609.  doi: 10.15388/namc.2021.26.23060.

[26]

Y. LuoZ. WangJ. LiangG. Wei and F. E. Alsaadi, $H_{\infty}$ control for 2-D fuzzy systems with interval time-varying delays and missing measurements, IEEE Trans. Cybern., 47 (2017), 365-377. 

[27]

D. H. Owens and E. Rogers, Stability analysis for a class of 2D continuous-discrete linear systems with dynamic boundary conditions, Syst. Control Lett., 37 (1999), 55-60.  doi: 10.1016/S0167-6911(99)00008-0.

[28]

W. QinG. WangL. Li and M. Shen, Fault detection for 2-D continuous-discrete state-delayed systems in finite frequency domains, IEEE Access, 8 (2020), 103141-103148.  doi: 10.1109/ACCESS.2020.2999565.

[29]

Y. RenD.-W. Ding and Q. Li, Finite-frequency fault detection for two-dimensional Fornasini-Marchesini dynamical systems, Int. J. Syst. Sci., 48 (2017), 2610-2621.  doi: 10.1080/00207721.2017.1333169.

[30]

R. P. Roesser, A discrete state-space model for linear image processing, IEEE Trans. Autom. Control, AC-20 (1975), 1-10.  doi: 10.1109/tac.1975.1100844.

[31]

T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man. Cybern., SMC-15 (1985), 116-132.  doi: 10.1016/B978-1-4832-1450-4.50045-6.

[32]

E. TianZ. WangL. Zou and D. Yue, Chance-constrained $H_{\infty}$ control for a class of time-varying systems with stochastic nonlinearities: the finite-horizon case, Automatica, 107 (2019), 296-305.  doi: 10.1016/j.automatica.2019.05.039.

[33]

K. Wan, Iterative learning control of two-dimensional discrete systems in General model, Nonlinear Dynam., 104 (2021), 1315-1327.  doi: 10.1007/s11071-021-06326-1.

[34]

F. Wang, Z. Wang, J. Liang and X. Liu, Recursive state estimation for two-dimensional shift-varying systems with random parameter perturbation and dynamical bias, Automatica J. IFAC, 112 (2020), 108658, 12 pp. doi: 10.1016/j.automatica.2019.108658.

[35]

L. WangW. WangG. Zhang and W. Chen, Generalised Kalman-Yakubovich-Popov lemma with its application in finite frequency positive realness control for two-dimensional continuous-discrete systems in the Roesser model form, IET Control Theory Appl., 9 (2015), 1676-1682.  doi: 10.1049/iet-cta.2014.0875.

[36]

Y. WangL. ZouL. MaZ. Zhao and J. Guo, A survey on control for Takagi-Sugeno fuzzy systems subject to engineering-oriented complexities, Syst. Sci. Control Eng., 9 (2021), 334-349.  doi: 10.1080/21642583.2021.1907259.

[37]

Q. WuQ. SongZ. ZhaoY. Liu and F. E. Alsaadi, Stabilization of T-S fuzzy fractional rectangular descriptor time-delay system, Int. J. Syst. Sci., 52 (2021), 2268-2282.  doi: 10.1080/00207721.2021.1882613.

[38]

X.-P. XieD. Yang and H. Ma, Observer design of discrete-time T-S fuzzy systems via multi-instant homogenous matrix polynomials, IEEE Trans. Fuzzy Syst., 22 (2014), 1714-1719. 

[39]

H. YangY. Xia and B. Liu, Fault detection for T-S fuzzy discrete systems in finite-frequency domain, IEEE Trans. Syst., Man., Cybern., Cybern., 41 (2011), 911-920. 

[40]

D. ZhaoC. K. AhnW. PaszkeF. Fu and Y. Li, Fault diagnosability analysis of two-dimensional linear discrete systems, IEEE Trans. Autom. Control, 66 (2021), 826-832.  doi: 10.1109/TAC.2020.2986054.

[41]

C. Zhu, X. Li and J. Cao, Finite-time $H_{\infty}$ dynamic output feedback control for nonlinear impulsive switched systems, Nonlinear Anal. Hybri. Syst., 39 (2021), 100975, 13 pp. doi: 10.1016/j.nahs.2020.100975.

[42]

K. ZhuJ. HuY. LiuN. D. Alotaibi and F. E. Alsaadi, On $\ell_{2}$-$\ell_{\infty}$ output-feedback control scheduled by stochastic communication protocol for two-dimensional switched systems, Int. J. Syst. Sci., 52 (2021), 2961-2976.  doi: 10.1080/00207721.2021.1914768.

show all references

References:
[1]

S. E. BentonE. Rogers and D. H. Owens, Stability conditions for a class of 2D continuous-discrete linear systems with dynamic boundary conditions, Int. J. Control, 75 (2002), 52-60.  doi: 10.1080/00207170110086962.

[2]

J. Chen and R. J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Dordrecht, 1999. doi: 10.1007/978-1-4615-5149-2.

[3]

Y. ChenW. Zhang and H. Gao, Finite frequency $H_{\infty}$ control for building under earthquake excitation, Mechatronics, 20 (2010), 128-142. 

[4]

G. Chesi and R. H. Middleton, Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty, Automatica J. IFAC, 67 (2016), 233-243.  doi: 10.1016/j.automatica.2016.01.042.

[5]

G. Chesi and R. H. Middleton, Necessary and sufficient LMI conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems, IEEE Trans. Autom. Control, 59 (2014), 996-1007.  doi: 10.1109/TAC.2014.2299353.

[6]

D. DingQ.-L. HanZ. Wang and X. Ge, A survey on model-based distributed control and filtering for industrial cyber-physical systems, IEEE Trans. Ind. Inform., 15 (2019), 2483-2499.  doi: 10.1109/TII.2019.2905295.

[7]

D.-W. Ding and G.-H. Yang, Fuzzy filter design for nonlinear systems in finite-frequency domain, IEEE Trans. Fuzzy Syst., 18 (2010), 935-945.  doi: 10.1109/TFUZZ.2010.2058807.

[8]

C. DuL. XieG. Guo and J. N. Teoh, A generalized KYP lemma based approach for disturbance rejection in data storage systems, Automatica J. IFAC, 43 (2007), 2112-2118.  doi: 10.1016/j.automatica.2007.04.023.

[9]

Z. DuanI. Ghous and J. Shen, Fault detection observer design for discrete-time 2-D T-S fuzzy systems with finite-frequency specifications, Fuzzy Set. Syst., 392 (2020), 24-45.  doi: 10.1016/j.fss.2019.05.004.

[10]

G. Feng, Analysis and Synthesis of Fuzzy Control Systems: A Modeled-Based Approach, Taylor & Francis Group, Boca Raton, 2010.

[11]

E. Fornasini and G. Marchesini, State-space realization theory of two-dimensional filters, IEEE Trans. Autom. Control, AC-21 (1976), 484-492.  doi: 10.1109/tac.1976.1101305.

[12]

D. Franke, 2D-Analysis of Hybrid Systems, Advances in Control, Springer, London, (1999), 293–299.

[13]

T. Iwasaki and S. Hara, Generalized KYP lemma: Unified frequency domain inequalities with design applications, IEEE Trans. Autom. Control, 50 (2005), 41-59.  doi: 10.1109/TAC.2004.840475.

[14]

T. IwasakiS. Hara and A. L. Fradkov, Time domain interpretations of frequency domain inequalities on (semi)finite ranges, Syst. Control Lett., 54 (2005), 681-691.  doi: 10.1016/j.sysconle.2004.11.007.

[15]

T. Kaczorek, Two-Dimensional Linear Systems, Lecture Notes in Control and Information Sciences, 68. Springer-Verlag Berlin, Heidelberg, 1985.

[16]

S. H. Kim and P. Park, $H_{\infty}$ state-feedback-control design for discrete-time fuzzy systems using relaxation technique for parameterized LMI, IEEE Trans. Fuzzy Syst., 18 (2010), 985-993. 

[17]

S. Knorn, A Two-Dimensional Systems Stability Analysis of Vehicle Platoons, PhD Thesis, National University of Ireland Maynooth, 2013.

[18]

S. Knorn and R. H. Middleton, Asymptotic and exponential stability of nonlinear two-dimensional continuous-discrete Roesser models, Syst. Control Lett., 93 (2016), 35-42.  doi: 10.1016/j.sysconle.2016.03.004.

[19]

S. Knorn and R. H. Middleton, Stability of two-dimensional linear systems with singularities on the stability boundary using LMIs, IEEE Trans. Autom. Control, 58 (2013), 2579-2590.  doi: 10.1109/TAC.2013.2264852.

[20]

D. LiJ. Liang and F. Wang, Robust $H_{\infty}$ filtering for 2D systems with RON under the stochastic communication protocol, IET Control Theory Appl., 14 (2020), 2795-2804. 

[21]

L. LiS. X. DingJ. QiuY. Yang and D. Xu, Fuzzy observer-based fault detection design approach for nonlinear processes, IEEE Trams. Syst., Man., Cybern., Syst., 47 (2017), 1941-1952. 

[22]

L. Li and W. Wang, Fuzzy modeling and $H_{\infty}$ control for general 2D nonlinear systems, Fuzzy Set. Syst., 207 (2012), 1-26.  doi: 10.1016/j.fss.2012.04.002.

[23]

J. LiangJ. Wang and T. Huang, $l_1$ filtering for continuous-discrete T-S fuzzy positive Roesser model, J. Franklin Inst., 355 (2018), 7281-7305.  doi: 10.1016/j.jfranklin.2018.07.017.

[24]

X. LiangJ. XiaG. ChenH. Zhang and Z. Wang, $H_{\infty}$ control for fuzzy Markovian jump systems based on sampled-data control method, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 1329-1343.  doi: 10.3934/dcdss.2020368.

[25]

S. LiuL. ZhaoW. ZhangX. Yang and F. E. Alsaadi, Fast fixed-time synchronization of T-S fuzzy complex networks, Nonlinear Anal. Model. Control, 26 (2021), 597-609.  doi: 10.15388/namc.2021.26.23060.

[26]

Y. LuoZ. WangJ. LiangG. Wei and F. E. Alsaadi, $H_{\infty}$ control for 2-D fuzzy systems with interval time-varying delays and missing measurements, IEEE Trans. Cybern., 47 (2017), 365-377. 

[27]

D. H. Owens and E. Rogers, Stability analysis for a class of 2D continuous-discrete linear systems with dynamic boundary conditions, Syst. Control Lett., 37 (1999), 55-60.  doi: 10.1016/S0167-6911(99)00008-0.

[28]

W. QinG. WangL. Li and M. Shen, Fault detection for 2-D continuous-discrete state-delayed systems in finite frequency domains, IEEE Access, 8 (2020), 103141-103148.  doi: 10.1109/ACCESS.2020.2999565.

[29]

Y. RenD.-W. Ding and Q. Li, Finite-frequency fault detection for two-dimensional Fornasini-Marchesini dynamical systems, Int. J. Syst. Sci., 48 (2017), 2610-2621.  doi: 10.1080/00207721.2017.1333169.

[30]

R. P. Roesser, A discrete state-space model for linear image processing, IEEE Trans. Autom. Control, AC-20 (1975), 1-10.  doi: 10.1109/tac.1975.1100844.

[31]

T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man. Cybern., SMC-15 (1985), 116-132.  doi: 10.1016/B978-1-4832-1450-4.50045-6.

[32]

E. TianZ. WangL. Zou and D. Yue, Chance-constrained $H_{\infty}$ control for a class of time-varying systems with stochastic nonlinearities: the finite-horizon case, Automatica, 107 (2019), 296-305.  doi: 10.1016/j.automatica.2019.05.039.

[33]

K. Wan, Iterative learning control of two-dimensional discrete systems in General model, Nonlinear Dynam., 104 (2021), 1315-1327.  doi: 10.1007/s11071-021-06326-1.

[34]

F. Wang, Z. Wang, J. Liang and X. Liu, Recursive state estimation for two-dimensional shift-varying systems with random parameter perturbation and dynamical bias, Automatica J. IFAC, 112 (2020), 108658, 12 pp. doi: 10.1016/j.automatica.2019.108658.

[35]

L. WangW. WangG. Zhang and W. Chen, Generalised Kalman-Yakubovich-Popov lemma with its application in finite frequency positive realness control for two-dimensional continuous-discrete systems in the Roesser model form, IET Control Theory Appl., 9 (2015), 1676-1682.  doi: 10.1049/iet-cta.2014.0875.

[36]

Y. WangL. ZouL. MaZ. Zhao and J. Guo, A survey on control for Takagi-Sugeno fuzzy systems subject to engineering-oriented complexities, Syst. Sci. Control Eng., 9 (2021), 334-349.  doi: 10.1080/21642583.2021.1907259.

[37]

Q. WuQ. SongZ. ZhaoY. Liu and F. E. Alsaadi, Stabilization of T-S fuzzy fractional rectangular descriptor time-delay system, Int. J. Syst. Sci., 52 (2021), 2268-2282.  doi: 10.1080/00207721.2021.1882613.

[38]

X.-P. XieD. Yang and H. Ma, Observer design of discrete-time T-S fuzzy systems via multi-instant homogenous matrix polynomials, IEEE Trans. Fuzzy Syst., 22 (2014), 1714-1719. 

[39]

H. YangY. Xia and B. Liu, Fault detection for T-S fuzzy discrete systems in finite-frequency domain, IEEE Trans. Syst., Man., Cybern., Cybern., 41 (2011), 911-920. 

[40]

D. ZhaoC. K. AhnW. PaszkeF. Fu and Y. Li, Fault diagnosability analysis of two-dimensional linear discrete systems, IEEE Trans. Autom. Control, 66 (2021), 826-832.  doi: 10.1109/TAC.2020.2986054.

[41]

C. Zhu, X. Li and J. Cao, Finite-time $H_{\infty}$ dynamic output feedback control for nonlinear impulsive switched systems, Nonlinear Anal. Hybri. Syst., 39 (2021), 100975, 13 pp. doi: 10.1016/j.nahs.2020.100975.

[42]

K. ZhuJ. HuY. LiuN. D. Alotaibi and F. E. Alsaadi, On $\ell_{2}$-$\ell_{\infty}$ output-feedback control scheduled by stochastic communication protocol for two-dimensional switched systems, Int. J. Syst. Sci., 52 (2021), 2961-2976.  doi: 10.1080/00207721.2021.1914768.

Figure 1.  The state trajectory of $ x_h\left( {t,k} \right) $
Figure 2.  The state trajectory of $ x_v\left( {t,k} \right) $
Figure 3.  The controlled output $ y\left( {t,k} \right) $
[1]

Ramalingam Sakthivel, Palanisamy Selvaraj, Yeong-Jae Kim, Dong-Hoon Lee, Oh-Min Kwon, Rathinasamy Sakthivel. Robust $ H_\infty $ resilient event-triggered control design for T-S fuzzy systems. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022028

[2]

Canghua Jiang, Dongming Zhang, Chi Yuan, Kok Ley Teo. An active set solver for constrained $ H_\infty $ optimal control problems with state and input constraints. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 135-157. doi: 10.3934/naco.2021056

[3]

Liqiang Jin, Yanyan Yin, Kok Lay Teo, Fei Liu. Event-triggered mixed $ H_\infty $ and passive control for Markov jump systems with bounded inputs. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1343-1355. doi: 10.3934/jimo.2020024

[4]

Junlin Xiong, Wenjie Liu. $ H_{\infty} $ observer-based control for large-scale systems with sparse observer communication network. Numerical Algebra, Control and Optimization, 2020, 10 (3) : 331-343. doi: 10.3934/naco.2020005

[5]

Xingyue Liang, Jianwei Xia, Guoliang Chen, Huasheng Zhang, Zhen Wang. $ \mathcal{H}_{\infty} $ control for fuzzy markovian jump systems based on sampled-data control method. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1329-1343. doi: 10.3934/dcdss.2020368

[6]

Jamal Mrazgua, El Houssaine Tissir, Mohamed Ouahi. Frequency domain $ H_{\infty} $ control design for active suspension systems. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 197-212. doi: 10.3934/dcdss.2021036

[7]

Ta T.H. Trang, Vu N. Phat, Adly Samir. Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback. Journal of Industrial and Management Optimization, 2016, 12 (1) : 303-315. doi: 10.3934/jimo.2016.12.303

[8]

Lin Du, Yun Zhang. $\mathcal{H}_∞$ filtering for switched nonlinear systems: A state projection method. Journal of Industrial and Management Optimization, 2018, 14 (1) : 19-33. doi: 10.3934/jimo.2017035

[9]

M. S. Mahmoud, P. Shi, Y. Shi. $H_\infty$ and robust control of interconnected systems with Markovian jump parameters. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 365-384. doi: 10.3934/dcdsb.2005.5.365

[10]

Tadahisa Funaki, Yueyuan Gao, Danielle Hilhorst. Convergence of a finite volume scheme for a stochastic conservation law involving a $Q$-brownian motion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1459-1502. doi: 10.3934/dcdsb.2018159

[11]

Irena Lasiecka, Buddhika Priyasad, Roberto Triggiani. Uniform stabilization of Boussinesq systems in critical $ \mathbf{L}^q $-based Sobolev and Besov spaces by finite dimensional interior localized feedback controls. Discrete and Continuous Dynamical Systems - B, 2020, 25 (10) : 4071-4117. doi: 10.3934/dcdsb.2020187

[12]

Joackim Bernier. Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on $ h\mathbb{Z} $. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3179-3195. doi: 10.3934/dcds.2019131

[13]

Li-Min Wang, Jing-Xian Yu, Jia Shi, Fu-Rong Gao. Delay-range dependent $H_\infty$ control for uncertain 2D-delayed systems. Numerical Algebra, Control and Optimization, 2015, 5 (1) : 11-23. doi: 10.3934/naco.2015.5.11

[14]

Rong Zhang. Nonexistence of Positive Solutions for high-order Hardy-H$ \acute{e} $non Systems on $ \mathbb{R}^{n} $. Communications on Pure and Applied Analysis, 2022, 21 (8) : 2857-2872. doi: 10.3934/cpaa.2022078

[15]

Abdallah Benabdallah, Mohsen Dlala. Rapid exponential stabilization by boundary state feedback for a class of coupled nonlinear ODE and $ 1-d $ heat diffusion equation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1085-1102. doi: 10.3934/dcdss.2021092

[16]

Luca Battaglia, Francesca Gladiali, Massimo Grossi. Asymptotic behavior of minimal solutions of $ -\Delta u = \lambda f(u) $ as $ \lambda\to-\infty $. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 681-700. doi: 10.3934/dcds.2020293

[17]

Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195

[18]

JinHyon Kim, HyonHui Ju, WiJong An. Inheritance of $ {\mathscr F}- $chaos and $ {\mathscr F}- $sensitivities under an iteration for non-autonomous discrete systems. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022053

[19]

Zhong-Qiang Wu, Xi-Bo Zhao. Frequency $H_{2}/H_{∞}$ optimizing control for isolated microgrid based on IPSO algorithm. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1565-1577. doi: 10.3934/jimo.2018021

[20]

Wensheng Yin, Jinde Cao, Guoqiang Zheng. Further results on stabilization of stochastic differential equations with delayed feedback control under $ G $-expectation framework. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 883-901. doi: 10.3934/dcdsb.2021072

2021 Impact Factor: 1.865

Metrics

  • PDF downloads (166)
  • HTML views (135)
  • Cited by (0)

Other articles
by authors

[Back to Top]