On Robust stability of singular systems with random abrupt changes

Nonlinear Analysis, Theory, Methods and Applications

Volumn 63, Issue 3, 2005, Pages 301-310

  Boukas, E K ^a  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

Jump linear systems; Linear matrix inequality; Robust stochastic stability; Singular systems; Stochastic stability

Indexed keywords

LINEAR SYSTEMS; RANDOM PROCESSES; ROBUSTNESS (CONTROL SYSTEMS);

JUMP LINEAR SYSTEMS; LINEAR MATRIX INEQUALITY; ROBUST STOCHASTIC STABILITY; SINGULAR SWITCHING; STOCHASTIC STABILITY;

MARKOV PROCESSES;

EID: 24344487926     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.03.110     Document Type: Article

References (29)

1. E.K. Boukas, and H. Hang Exponential stability of stochastic systems with Markovian jumping parameters Automatica 35 1999 1437 1441
2. E.K. Boukas, and Z.K. Liu Robust H ∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays IEEE Trans. Automat. Control 46 2001 1918 1924
3. E.K. Boukas, and Z.K. Liu Robust stability and stability of Markov jump linear uncertain systems with mode-dependent time delays J. Optim. Theory Appl. 209 2001 587 600
4. E.K. Boukas, and Z.K. Liu Deterministic and Stochastic Systems with Time-Delay 2002 Birkhauser Boston
5. E.K. Boukas, and Z.K. Liu Delay-dependent stability analysis of singular linear continuous-time systems IEE Proc. Control Theory Appl. 150 2 2003 325 330
6. E.K. Boukas, and Z.K. Liu Delay-dependent stabilization of singularly perturbed jump linear systems Int. J. Control 77 3 2004 310 319
7. E.K. Boukas, Z.K. Liu, and G.X. Liu Delay-dependent robust stability and H ∞ control of jump linear systems with time-delay Int. J. Control 74 2001 329 340
8. Y.Y. Cao, and J. Lam Robust H ∞ control of uncertain Markovian jump systems with time-delay IEEE Trans. Automat. Control 45 1 2000
9. L. Dai, Singular control systems, Lecture Notes in Control and Information Sciences, vol. 118, Springer, New York, 1989.
10. C.E. de Souza, and M.D. Fragoso Robust H ∞ filtering for Markovian jump linear systems Proceedings of the 35th IEEE Conference on Decision and Control Kobe, Japan December 1996 4808 4813
11. X. Feng, K.A. Loparo, Y. Ji, and H.J. Chizeck Stochastic stability properties of jump linear systems IEEE Trans. Automat. Control 37 1992 38 53
12. L.R. Fletcher Pole assignment and controllability subspaces in descriptor systems Int. J. Control 66 1997 677 709
13. E. Fridman A Lyapunov-based approach to stability of descriptor systems with delay Proceedings of the 40th IEEE Conference on Control and Decision Orlando, Florida, USA December 2001 2850 2855
14. Y. Ji, and H.J. Chizeck Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control IEEE Trans. Automat. Control 35 1990 777 788
15. A. Kumar, and P. Daoutidis Feedback control of nonlinear differential-algebraic equation systems AIChE J. 41 1995 619 636
16. W. Lan, and J. Huang Semiglobal stabilization and output regulation of singular linear systems with input saturation IEEE Trans. Automat. Control 48 7 2003 1274 1280
17. F.L. Lewis A survey of linear singular systems Circuits Systems Signal Process. 5 1986 3 36
18. X. Mao Stability of stochastic differential equations with Markovian switching Stochastic Process. Appl. 79 1999 45 67
19. M. Mariton Control of nonlinear systems with Markovian parameter changes IEEE Trans. Automat. Control 36 1991 233 238
20. R.W. Newcomb The semistate description of nonlinear time-variable circuits IEEE Trans. Circuits and Systems 28 1981 62 71
21. P. Shi, and E.K. Boukas H ∞ -control for Markovian jumping linear systems with parametric uncertainty J. Optim. Theory Appl. 95 1997 75 99
22. P. Shi, and E.K. Boukas On H ∞ control design for singular continuous-time delay systems with parametric uncertainties Nonlinear Dynamics Systems Theory 4 1 2004 59 71
23. K. Takaba, N. Morihira, and T. Katayama A generalized Lyapunov theorem for descriptor system Systems Control Lett. 24 1995 49 51
24. G.C. Verghese, B.C. Levy, and T. Kailath A generalized state-space for singular systems IEEE Trans. Automat. Control 26 1981 811 831
25. S. Xu, P.V. Dooren, R. Stefan, and J. Lam Robust stability and stabilization of discrete-time singular systems with state delay and parameter uncertainty IEEE Trans. Automat. Control 47 7 2002 1122 1128
26. S. Xu, and J. Lam Robust stability for uncertain discrete singular systems with state delay Asian J. Control 5 2003 399 405
27. S. Xu, and J. Lam Robust stability and stabilization of discrete-time singular systems: an equivalent characterization IEEE Trans. Automat. Control 49 4 2004 568 574
28. S. Xu, J. Lam, and L. Zhang Robust D-stability analysis for uncertain discrete singular systems with state delay IEEE Trans. Circuits and Systems I 49 2002 551 555
29. S. Xu, C. Yang, Stabilization of discrete-time singular systems: a matrix inequalities approach, Automatica 35 (1999) 1613-1617, 776-783.