-
Previous Article
An alternating direction method for solving a class of inverse semi-definite quadratic programming problems
- JIMO Home
- This Issue
-
Next Article
Subgradient-based neural network for nonconvex optimization problems in support vector machines with indefinite kernels
Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback
1. | Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi 10307, Vietnam, Vietnam |
2. | Université de Limoges, Laboratoire XLIM, 123, avenue Albert Thomas, 87060 Limoges CEDEX, France |
References:
[1] |
F. Amato, M. Ariola and C. Cosentino, Finite-time stabilization via dynamic output feedback, Automatica, 42 (2006), 337-342.
doi: 10.1016/j.automatica.2005.09.007. |
[2] |
F. Amato, G. De Tommasi and A. Pironti, Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems, Automatica, 49 (2013), 2546-2550.
doi: 10.1016/j.automatica.2013.04.004. |
[3] |
E. K. Boukas, Static output feedback control for stochastic hybrid systems: LMI approach, Automatica, 42 (2006), 183-188.
doi: 10.1016/j.automatica.2005.08.012. |
[4] |
S. Boyd, L. El. Ghaoui and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.
doi: 10.1137/1.9781611970777. |
[5] |
P. Dorato, Short time stability in linear time-varying systems, In Proc IRE Int Convention Record, 4 (1961), 83-87. |
[6] |
E. Fridman and U. Shaked, Delay-dependent stability and $H_{\infty}$control: constant and time-varying delays, International Journal of Control, 76 (2003), 48-60.
doi: 10.1080/0020717021000049151. |
[7] |
P. Gahinet, A. Nemirovskii, A. J. Laub and M. Chilali, LMI Control Toolbox For use with MATLAB, The MathWorks, Inc, 1995. |
[8] |
G. Garcia, S. Tarbouriech and J. Bernussou, Finite-time stabilization of linear time-varying continuous systems, IEEE Transactions on Automatic Control, 54 (2009), 364-369.
doi: 10.1109/TAC.2008.2008325. |
[9] |
L. Gollmann and H. Maurer, Theory and applications of optimal control problems with multiple time-delays, Journal of Industrial and Management Optimization, 10 (2014), 413-441. |
[10] |
V. Kharitonov, Time-Delay Systems: Lyapunov Functionals and Matrices, Control Engineering. Birkhäuser/Springer, New York, 2013. |
[11] |
O. M. Kwon, J. H. Park and S. M. Lee, Exponential stability for uncertain dynamic systems with time-varying delays: LMI optimization approach, Journal of Optimization Theory and Applications, 137 (2008), 521-532.
doi: 10.1007/s10957-008-9357-7. |
[12] |
H. Liu, Y. Shen and X. Zhao, Delay-dependent observer-based $H_\infty$ finite-time control for switched systems with time-varying delay, Nonlinear Analysis: Hybrid Systems, 6 (2012), 885-898.
doi: 10.1016/j.nahs.2012.03.001. |
[13] |
Q. Y. Meng and Y. J Shen, Finite-time $H_\infty$ control for linear continuous system with norm-bounded disturbance, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 1043-1049.
doi: 10.1016/j.cnsns.2008.03.010. |
[14] |
E. Moulay, M. Dambrine, N. Yeganefar and W. Perruquetti, Finite-time stability and stabilization of time-delay systems, Systems and Control Letters, 57 (2008), 561-566.
doi: 10.1016/j.sysconle.2007.12.002. |
[15] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays, Journal of Optimization Theory and Applications,151 (2011), 100-120.
doi: 10.1007/s10957-011-9858-7. |
[16] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays, Journal of Optimization Theory and Applications, 151 (2011), 100-120.
doi: 10.1007/s10957-011-9858-7. |
[17] |
A. Seuret and F. Gouaisbaut, Wirtinger-based integral inequality: Application to time-delay systems, Automatica, 49 (2013), 2860-2866.
doi: 10.1016/j.automatica.2013.05.030. |
[18] |
L. Wu, J. Lam and C. Wang, Robust $H_{\infty}$ dynamic output feedback control for 2D linear parameter-varying systems, IMA journal of mathematical control and information, 26 (2009), 23-44.
doi: 10.1093/imamci/dnm028. |
[19] |
Z. Xiang, Y. N. Sun and M. S. Mahmoud, Robust finite-time $H_\infty$ control for a class of uncertain switched neutral systems, Communications in Nonlinear Science Numerical Simulations, 17 (2012), 1766-1778.
doi: 10.1016/j.cnsns.2011.09.022. |
[20] |
W. Xiang and J. Xiao, $H_{\infty}$ finite-time control for nonlinear switched discrete-time systems with norm-bounded disturbance, Journal of the Franklin Institute, 348 (2011), 331-352.
doi: 10.1016/j.jfranklin.2010.12.001. |
[21] |
H. Xu and K. L. Teo, $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach, Journal of Industrial and Management Optimization, 5 (2009), 153-159.
doi: 10.3934/jimo.2009.5.153. |
[22] |
Y. Zhang, C. Liu and X. Mu, Robust finite-time $H_\infty$ control of singular stochastic systems via static output feedback, Applied Mathematics and Computation, 218 (2012), 5629-5640.
doi: 10.1016/j.amc.2011.11.057. |
show all references
References:
[1] |
F. Amato, M. Ariola and C. Cosentino, Finite-time stabilization via dynamic output feedback, Automatica, 42 (2006), 337-342.
doi: 10.1016/j.automatica.2005.09.007. |
[2] |
F. Amato, G. De Tommasi and A. Pironti, Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems, Automatica, 49 (2013), 2546-2550.
doi: 10.1016/j.automatica.2013.04.004. |
[3] |
E. K. Boukas, Static output feedback control for stochastic hybrid systems: LMI approach, Automatica, 42 (2006), 183-188.
doi: 10.1016/j.automatica.2005.08.012. |
[4] |
S. Boyd, L. El. Ghaoui and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.
doi: 10.1137/1.9781611970777. |
[5] |
P. Dorato, Short time stability in linear time-varying systems, In Proc IRE Int Convention Record, 4 (1961), 83-87. |
[6] |
E. Fridman and U. Shaked, Delay-dependent stability and $H_{\infty}$control: constant and time-varying delays, International Journal of Control, 76 (2003), 48-60.
doi: 10.1080/0020717021000049151. |
[7] |
P. Gahinet, A. Nemirovskii, A. J. Laub and M. Chilali, LMI Control Toolbox For use with MATLAB, The MathWorks, Inc, 1995. |
[8] |
G. Garcia, S. Tarbouriech and J. Bernussou, Finite-time stabilization of linear time-varying continuous systems, IEEE Transactions on Automatic Control, 54 (2009), 364-369.
doi: 10.1109/TAC.2008.2008325. |
[9] |
L. Gollmann and H. Maurer, Theory and applications of optimal control problems with multiple time-delays, Journal of Industrial and Management Optimization, 10 (2014), 413-441. |
[10] |
V. Kharitonov, Time-Delay Systems: Lyapunov Functionals and Matrices, Control Engineering. Birkhäuser/Springer, New York, 2013. |
[11] |
O. M. Kwon, J. H. Park and S. M. Lee, Exponential stability for uncertain dynamic systems with time-varying delays: LMI optimization approach, Journal of Optimization Theory and Applications, 137 (2008), 521-532.
doi: 10.1007/s10957-008-9357-7. |
[12] |
H. Liu, Y. Shen and X. Zhao, Delay-dependent observer-based $H_\infty$ finite-time control for switched systems with time-varying delay, Nonlinear Analysis: Hybrid Systems, 6 (2012), 885-898.
doi: 10.1016/j.nahs.2012.03.001. |
[13] |
Q. Y. Meng and Y. J Shen, Finite-time $H_\infty$ control for linear continuous system with norm-bounded disturbance, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 1043-1049.
doi: 10.1016/j.cnsns.2008.03.010. |
[14] |
E. Moulay, M. Dambrine, N. Yeganefar and W. Perruquetti, Finite-time stability and stabilization of time-delay systems, Systems and Control Letters, 57 (2008), 561-566.
doi: 10.1016/j.sysconle.2007.12.002. |
[15] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays, Journal of Optimization Theory and Applications,151 (2011), 100-120.
doi: 10.1007/s10957-011-9858-7. |
[16] |
T. Senthilkumar and P. Balasubramaniam, Delay-dependent robust stabilization and $H_\infty$ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays, Journal of Optimization Theory and Applications, 151 (2011), 100-120.
doi: 10.1007/s10957-011-9858-7. |
[17] |
A. Seuret and F. Gouaisbaut, Wirtinger-based integral inequality: Application to time-delay systems, Automatica, 49 (2013), 2860-2866.
doi: 10.1016/j.automatica.2013.05.030. |
[18] |
L. Wu, J. Lam and C. Wang, Robust $H_{\infty}$ dynamic output feedback control for 2D linear parameter-varying systems, IMA journal of mathematical control and information, 26 (2009), 23-44.
doi: 10.1093/imamci/dnm028. |
[19] |
Z. Xiang, Y. N. Sun and M. S. Mahmoud, Robust finite-time $H_\infty$ control for a class of uncertain switched neutral systems, Communications in Nonlinear Science Numerical Simulations, 17 (2012), 1766-1778.
doi: 10.1016/j.cnsns.2011.09.022. |
[20] |
W. Xiang and J. Xiao, $H_{\infty}$ finite-time control for nonlinear switched discrete-time systems with norm-bounded disturbance, Journal of the Franklin Institute, 348 (2011), 331-352.
doi: 10.1016/j.jfranklin.2010.12.001. |
[21] |
H. Xu and K. L. Teo, $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach, Journal of Industrial and Management Optimization, 5 (2009), 153-159.
doi: 10.3934/jimo.2009.5.153. |
[22] |
Y. Zhang, C. Liu and X. Mu, Robust finite-time $H_\infty$ control of singular stochastic systems via static output feedback, Applied Mathematics and Computation, 218 (2012), 5629-5640.
doi: 10.1016/j.amc.2011.11.057. |
[1] |
K. Aruna Sakthi, A. Vinodkumar. Stabilization on input time-varying delay for linear switched systems with truncated predictor control. Numerical Algebra, Control and Optimization, 2020, 10 (2) : 237-247. doi: 10.3934/naco.2019050 |
[2] |
Zixiao Xiong, Xining Li, Qimin Zhang. Threshold dynamics and finite-time stability of reaction-diffusion vegetation-water systems in arid area with time-varying delay. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022138 |
[3] |
Aowen Kong, Carlos Nonato, Wenjun Liu, Manoel Jeremias dos Santos, Carlos Raposo. Equivalence between exponential stabilization and observability inequality for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 2959-2978. doi: 10.3934/dcdsb.2021168 |
[4] |
Peter Giesl. Construction of a finite-time Lyapunov function by meshless collocation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2387-2412. doi: 10.3934/dcdsb.2012.17.2387 |
[5] |
Shu Zhang, Jian Xu. Time-varying delayed feedback control for an internet congestion control model. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 653-668. doi: 10.3934/dcdsb.2011.16.653 |
[6] |
Baowei Feng, Carlos Alberto Raposo, Carlos Alberto Nonato, Abdelaziz Soufyane. Analysis of exponential stabilization for Rao-Nakra sandwich beam with time-varying weight and time-varying delay: Multiplier method versus observability. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022011 |
[7] |
Roberta Fabbri, Russell Johnson, Sylvia Novo, Carmen Núñez. On linear-quadratic dissipative control processes with time-varying coefficients. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 193-210. doi: 10.3934/dcds.2013.33.193 |
[8] |
Le Viet Cuong, Thai Son Doan. Assignability of dichotomy spectra for discrete time-varying linear control systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3597-3607. doi: 10.3934/dcdsb.2020074 |
[9] |
Sanjeeva Balasuriya. Uncertainty in finite-time Lyapunov exponent computations. Journal of Computational Dynamics, 2020, 7 (2) : 313-337. doi: 10.3934/jcd.2020013 |
[10] |
Ling Zhang, Xiaoqi Sun. Stability analysis of time-varying delay neural network for convex quadratic programming with equality constraints and inequality constraints. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022035 |
[11] |
Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of a network of strings. Mathematical Control and Related Fields, 2015, 5 (4) : 721-742. doi: 10.3934/mcrf.2015.5.721 |
[12] |
Di Wu, Yanqin Bai, Fusheng Xie. Time-scaling transformation for optimal control problem with time-varying delay. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1683-1695. doi: 10.3934/dcdss.2020098 |
[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] |
Mokhtari Yacine. Boundary controllability and boundary time-varying feedback stabilization of the 1D wave equation in non-cylindrical domains. Evolution Equations and Control Theory, 2022, 11 (2) : 373-397. doi: 10.3934/eect.2021004 |
[15] |
Carlos Nonato, Manoel Jeremias dos Santos, Carlos Raposo. Dynamics of Timoshenko system with time-varying weight and time-varying delay. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 523-553. doi: 10.3934/dcdsb.2021053 |
[16] |
Khalid Addi, Samir Adly, Hassan Saoud. Finite-time Lyapunov stability analysis of evolution variational inequalities. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1023-1038. doi: 10.3934/dcds.2011.31.1023 |
[17] |
Yangzi Hu, Fuke Wu. The improved results on the stochastic Kolmogorov system with time-varying delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1481-1497. doi: 10.3934/dcdsb.2015.20.1481 |
[18] |
Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary time-varying delay. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 693-722. doi: 10.3934/dcdss.2011.4.693 |
[19] |
Arno Berger. On finite-time hyperbolicity. Communications on Pure and Applied Analysis, 2011, 10 (3) : 963-981. doi: 10.3934/cpaa.2011.10.963 |
[20] |
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 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]