-
Previous Article
Stabilization of discrete-time Markovian jump systems with partially unknown transition probabilities
- DCDS-B Home
- This Issue
-
Next Article
Numerical simulation of two-fluid flow and meniscus interface movement in the electromagnetic continuous steel casting process
Necessary and sufficient conditions for stability of impulsive switched linear systems
1. | Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845 |
2. | Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth, W.A. 6845 |
3. | School of Information Science and Engineering, Central South University, Changsha, 410083, China |
References:
[1] |
F. H. F. Leung, P. K. S. Tam and C. K. Li, The control of switching DC-DC converters - a general LWR problem, Industrial Electronics, IEEE Transactions on, 38 (1991), 65-71. |
[2] |
Z. Doulgeri and G. Iliadis, Stability of a contact task for a robotic arm modelled as a switched system, Control Theory & Applications, IET, 1 (2007), 844-853.
doi: 10.1049/iet-cta:20060191. |
[3] |
M. Petreczky, Reachability of linear switched systems: Differential geometric approach, Systems & Control Letters, 55 (2006), 112-118.
doi: 10.1016/j.sysconle.2005.06.001. |
[4] |
Z. Sun and S. S. Ge, Analysis and synthesis of switched linear control systems, Automatica J. IFAC, 41 (2005), 181-195.
doi: 10.1016/j.automatica.2004.09.015. |
[5] |
Z. Sun, S. S. Ge and T. H. Lee, Controllability and reachability criteria for switched linear systems, Automatica J. IFAC, 38 (2002), 775-786.
doi: 10.1016/S0005-1098(01)00267-9. |
[6] |
G. Xie and L. Wang, Controllability and stabilizability of switched linear systems, Systems & Control Letters, 48 (2003), 135-155.
doi: 10.1016/S0167-6911(02)00288-8. |
[7] |
J. Ezzine and A. H. Haddad, Controllability and observability of hybrid systems, International Journal of Control, 49 (1989), 2045-2055. |
[8] |
J. Daafouz, P. Riedinger and C. Iung, Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach, IEEE Transactions on Automatic Control, 47 (2002), 1883-1887.
doi: 10.1109/TAC.2002.804474. |
[9] |
R. A. Decarlo, M. S. Branicky, S. Pettersson and B. Lennartson, Perspectives and results on the stability and stabilizability of hybrid systems, Proceedings of the IEEE, 88 (2000), 1069-1082.
doi: 10.1109/5.871309. |
[10] |
L. Hai and P. J. Antsaklis, Stability and stabilizability of switched linear systems: A survey of recent results, IEEE Transactions on Automatic Control, 54 (2009), 308-322.
doi: 10.1109/TAC.2008.2012009. |
[11] |
D. Liberzon, "Switching in Systems and Control," Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 2003. |
[12] |
H. Xu, X. Liu and K. L. Teo, Delay independent stability criteria of impulsive switched systems with time-invariant delays, Mathematical and Computer Modelling, 47 (2008), 372-379.
doi: 10.1016/j.mcm.2007.04.011. |
[13] |
H. Xu, K. L. Teo and X. Liu, Robust stability analysis of guaranteed cost control for impulsive switched systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 38 (2008), 1419-1422.
doi: 10.1109/TSMCB.2008.925747. |
[14] |
D. Zheng, "Linear System Theory," Tsinghua University Press, Beijing, 1990. |
[15] |
Z. Sun and S. S. Ge, "Switched Linear Systems," Springer-Verlag, London, 2005. |
[16] |
Q. Lu and G. Jiang, The dynamics of a prey-predator model with impulsive state feedback control, Discrete and Continuous Dynamical Systems - Series B, 6 (2006), 1301-1320.
doi: 10.3934/dcdsb.2006.6.1301. |
[17] |
A. Anguraj and T. Paul, Existence and uniqueness of nonlinear impulsive integro-differential equations, Discrete and Continuous Dynamical Systems - Series B, 6 (2006), 1191-1198.
doi: 10.3934/dcdsb.2006.6.1191. |
show all references
References:
[1] |
F. H. F. Leung, P. K. S. Tam and C. K. Li, The control of switching DC-DC converters - a general LWR problem, Industrial Electronics, IEEE Transactions on, 38 (1991), 65-71. |
[2] |
Z. Doulgeri and G. Iliadis, Stability of a contact task for a robotic arm modelled as a switched system, Control Theory & Applications, IET, 1 (2007), 844-853.
doi: 10.1049/iet-cta:20060191. |
[3] |
M. Petreczky, Reachability of linear switched systems: Differential geometric approach, Systems & Control Letters, 55 (2006), 112-118.
doi: 10.1016/j.sysconle.2005.06.001. |
[4] |
Z. Sun and S. S. Ge, Analysis and synthesis of switched linear control systems, Automatica J. IFAC, 41 (2005), 181-195.
doi: 10.1016/j.automatica.2004.09.015. |
[5] |
Z. Sun, S. S. Ge and T. H. Lee, Controllability and reachability criteria for switched linear systems, Automatica J. IFAC, 38 (2002), 775-786.
doi: 10.1016/S0005-1098(01)00267-9. |
[6] |
G. Xie and L. Wang, Controllability and stabilizability of switched linear systems, Systems & Control Letters, 48 (2003), 135-155.
doi: 10.1016/S0167-6911(02)00288-8. |
[7] |
J. Ezzine and A. H. Haddad, Controllability and observability of hybrid systems, International Journal of Control, 49 (1989), 2045-2055. |
[8] |
J. Daafouz, P. Riedinger and C. Iung, Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach, IEEE Transactions on Automatic Control, 47 (2002), 1883-1887.
doi: 10.1109/TAC.2002.804474. |
[9] |
R. A. Decarlo, M. S. Branicky, S. Pettersson and B. Lennartson, Perspectives and results on the stability and stabilizability of hybrid systems, Proceedings of the IEEE, 88 (2000), 1069-1082.
doi: 10.1109/5.871309. |
[10] |
L. Hai and P. J. Antsaklis, Stability and stabilizability of switched linear systems: A survey of recent results, IEEE Transactions on Automatic Control, 54 (2009), 308-322.
doi: 10.1109/TAC.2008.2012009. |
[11] |
D. Liberzon, "Switching in Systems and Control," Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 2003. |
[12] |
H. Xu, X. Liu and K. L. Teo, Delay independent stability criteria of impulsive switched systems with time-invariant delays, Mathematical and Computer Modelling, 47 (2008), 372-379.
doi: 10.1016/j.mcm.2007.04.011. |
[13] |
H. Xu, K. L. Teo and X. Liu, Robust stability analysis of guaranteed cost control for impulsive switched systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 38 (2008), 1419-1422.
doi: 10.1109/TSMCB.2008.925747. |
[14] |
D. Zheng, "Linear System Theory," Tsinghua University Press, Beijing, 1990. |
[15] |
Z. Sun and S. S. Ge, "Switched Linear Systems," Springer-Verlag, London, 2005. |
[16] |
Q. Lu and G. Jiang, The dynamics of a prey-predator model with impulsive state feedback control, Discrete and Continuous Dynamical Systems - Series B, 6 (2006), 1301-1320.
doi: 10.3934/dcdsb.2006.6.1301. |
[17] |
A. Anguraj and T. Paul, Existence and uniqueness of nonlinear impulsive integro-differential equations, Discrete and Continuous Dynamical Systems - Series B, 6 (2006), 1191-1198.
doi: 10.3934/dcdsb.2006.6.1191. |
[1] |
Elena K. Kostousova. State estimation for linear impulsive differential systems through polyhedral techniques. Conference Publications, 2009, 2009 (Special) : 466-475. doi: 10.3934/proc.2009.2009.466 |
[2] |
Ugo Boscain, Grégoire Charlot, Mario Sigalotti. Stability of planar nonlinear switched systems. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 415-432. doi: 10.3934/dcds.2006.15.415 |
[3] |
Philippe Jouan, Said Naciri. Asymptotic stability of uniformly bounded nonlinear switched systems. Mathematical Control and Related Fields, 2013, 3 (3) : 323-345. doi: 10.3934/mcrf.2013.3.323 |
[4] |
Moussa Balde, Ugo Boscain. Stability of planar switched systems: The nondiagonalizable case. Communications on Pure and Applied Analysis, 2008, 7 (1) : 1-21. doi: 10.3934/cpaa.2008.7.1 |
[5] |
Baskar Sundaravadivoo. Controllability analysis of nonlinear fractional order differential systems with state delay and non-instantaneous impulsive effects. Discrete and Continuous Dynamical Systems - S, 2020, 13 (9) : 2561-2573. doi: 10.3934/dcdss.2020138 |
[6] |
Alexander Pimenov, Dmitrii I. Rachinskii. Linear stability analysis of systems with Preisach memory. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 997-1018. doi: 10.3934/dcdsb.2009.11.997 |
[7] |
Xiang Xie, Honglei Xu, Xinming Cheng, Yilun Yu. Improved results on exponential stability of discrete-time switched delay systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 199-208. doi: 10.3934/dcdsb.2017010 |
[8] |
Michael Basin, Pablo Rodriguez-Ramirez. An optimal impulsive control regulator for linear systems. Numerical Algebra, Control and Optimization, 2011, 1 (2) : 275-282. doi: 10.3934/naco.2011.1.275 |
[9] |
Xueyan Yang, Xiaodi Li, Qiang Xi, Peiyong Duan. Review of stability and stabilization for impulsive delayed systems. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1495-1515. doi: 10.3934/mbe.2018069 |
[10] |
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 |
[11] |
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 |
[12] |
Hongyan Yan, Yun Sun, Yuanguo Zhu. A linear-quadratic control problem of uncertain discrete-time switched systems. Journal of Industrial and Management Optimization, 2017, 13 (1) : 267-282. doi: 10.3934/jimo.2016016 |
[13] |
Xiaojun Zhou, Chunhua Yang, Weihua Gui. State transition algorithm. Journal of Industrial and Management Optimization, 2012, 8 (4) : 1039-1056. doi: 10.3934/jimo.2012.8.1039 |
[14] |
Peter Howard, Bongsuk Kwon. Spectral analysis for transition front solutions in Cahn-Hilliard systems. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 125-166. doi: 10.3934/dcds.2012.32.125 |
[15] |
Everaldo de Mello Bonotto, Daniela Paula Demuner. Stability and forward attractors for non-autonomous impulsive semidynamical systems. Communications on Pure and Applied Analysis, 2020, 19 (4) : 1979-1996. doi: 10.3934/cpaa.2020087 |
[16] |
Xinyi He, Jianlong Qiu, Xiaodi Li, Jinde Cao. A brief survey on stability and stabilization of impulsive systems with delayed impulses. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1797-1821. doi: 10.3934/dcdss.2022080 |
[17] |
Stepan Sorokin, Maxim Staritsyn. Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control. Numerical Algebra, Control and Optimization, 2017, 7 (2) : 201-210. doi: 10.3934/naco.2017014 |
[18] |
Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic mean-square stability properties for systems of linear stochastic delay differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1521-1531. doi: 10.3934/dcdsb.2013.18.1521 |
[19] |
Daniel Alpay, Eduard Tsekanovskiĭ. Subclasses of Herglotz-Nevanlinna matrix-valued functtons and linear systems. Conference Publications, 2001, 2001 (Special) : 1-13. doi: 10.3934/proc.2001.2001.1 |
[20] |
Canghua Jiang, Kok Lay Teo, Ryan Loxton, Guang-Ren Duan. A neighboring extremal solution for an optimal switched impulsive control problem. Journal of Industrial and Management Optimization, 2012, 8 (3) : 591-609. doi: 10.3934/jimo.2012.8.591 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]