Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis

Chaos, Solitons and Fractals

Volumn 34, Issue 2, 2007, Pages 394-404

  Gao, Huijun ^a   Lam, James ^b   Wang, Zidong ^c  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; LINEAR MATRIX INEQUALITIES; LINEAR PROGRAMMING; OPTIMIZATION; PROBLEM SOLVING; SYSTEMS ANALYSIS; TIME VARYING SYSTEMS;

DISCRETE STOCHASTIC SYSTEMS; MINIMIZATION PROBLEMS; NUMERICAL SOFTWARES; SEQUENTIAL LINEAR PROGRAMMING MATRIX METHOD (SLPMM);

LINEAR SYSTEMS;

EID: 34147129623     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.03.027     Document Type: Article

References (36)

1. Arnold L. Stochastic differential equations: theory and applications (1974), Wiley, New York
2. Basin M, Skliar M. Integral approach to optimal filtering and control of continuous processes with time-varying delays. In: Proc 40th conf decision control, Orlando, FL, 2001, p. 2911-6.
3. Boukas E.K. Stabilization of stochastic nonlinear hybrid systems. Int J Innov Comput Inform Control 1 (2005) 131-141
4. ∞ control of uncertain linear state-delayed systems. Automatica 35 (1999) 1313-1321
5. ∞ type control for discrete-time stochastic systems. Int J Robust Nonlinear Control 9 (1999) 923-948
6. El Ghaoui L., Oustry F., and Ait Rami M. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans Automat Control 42 8 (1997) 1171-1176
7. Esfahani S., and Petersen I.R. An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems. Int J Robust Nonlinear Control 10 (2000) 157-174
8. ∞ control of linear time-delay systems'. IEEE Trans Automat Control 48 3 (2003) 520-525
9. ∞ filtering for a class of uncertain nonlinear time-delay systems. IEEE Trans Automat Control 48 9 (2003) 1661-1666
10. ∞ control and filtering of discrete-time stochastic with multiplicative noise. Automatica 37 (2001) 409-417
11. Hausmann U.G. Optimal stationary control with state and control dependent noise. SIAM J Control Optim 9 (1971) 184-198
12. He Y., Wang Q., and Zheng W. Global robust stability for delayed neural networks with polytopic type uncertainties. Chaos, Solitons & Fractals 26 5 (2005) 1349-1354
13. He Y., Wu M., She J.H., and Liu G.P. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Trans Automat Control 49 5 (2004) 828-832
14. ∞. SIAM J Control Optim 36 5 (1998) 1504-1538
15. Hsiao F., and Pan S. Robust Kalman filter synthesis for uncertain multiple time-delay stochastic systems. J Dyn Syst Meas Contr 118 (1996) 803-808
16. Kubrusly C.S. On discrete stochastic bilinear systems stability. J Math Anal Appl 113 (1986) 36-58
17. Kushner H. Stochastic stability and control (1967), Academic Press, New York
18. Lee YS, Kwon WH. Delay-dependent robust stabilization of uncertain discrete-time state-delayed systems. In: Proc 15th triennial world congress, Barcelona, Spain, 2002.
19. ∞ output feedback controllers. SIAM J Control Optim 57 (2001) 1711-1735
20. Liao X., and Mao X. Exponential stability of stochastic delay interval systems. Syst Control Lett 40 (2000) 171-181
21. Lin C., Wang Q.G., and Lee T.H. Less conservative stability conditions for fuzzy large-scale systems with time delays. Chaos, Solitons & Fractals 29 5 (2006) 1147-1154
22. Liu H., Boukas E.K., Sun F., and Ho D.W.C. Controller design for Markov jumping systems subject to actuator saturation. Automatica 42 3 (2006) 459-465
23. ∞ filter for Markovian jumping systems with time delay. IEEE Trans Circuits Syst (II) 51 (2004) 607-612
24. Mao X., Koroleva N., and Rodkina A. Robust stability of uncertain stochastic differential delay equations. Syst Control Lett 35 (1998) 325-336
25. Mao X.R. Almost sure exponential stability of delay equations with damped stochastic perturbation. Stochast Anal Appl 19 (2001) 67-84
26. Moon Y.S., Park P., Kwon W.H., and Lee Y.S. Delay-dependent robust stabilization of uncertain state-delayed systems. Int J Control 74 (2001) 1447-1455
27. Niu Y., Ho D.W.C., and Lam J. Robust integral sliding mode control for uncertain stochastic systems with time-varying delay. Automatica 41 5 (2005) 873-880
28. Park P. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Trans Automat Control 44 4 (1999) 876-877
29. Ruan H., Yaz E.E., and Zhai T. Current output filter for state estimation of nonlinear stochastic systems with linear measurement. Int J Innov Comput Inform Control 1 2 (2005) 277-287
30. ∞ analysis of nonlinear stochastic time-delay systems. Chaos, Solitons & Fractals 26 2 (2005) 637-647
31. ∞ observer design of linear state delayed systems with parametric uncertainty: the discrete-time case. Automatica 35 (1999) 1161-1167
32. Wang Z., and Qiao H. Robust filtering for bilinear uncertain stochastic discrete-time systems. IEEE Trans Signal Process 50 3 (2002) 560-567
33. Wonham W.M. On a matrix Riccati equation of stochastic control. SIAM J Control Optim 6 (1968) 681-697
34. Xie S., and Xie L. Stabilization of a class of uncertain large-scale stochastic systems with time delays. Automatica 36 (2000) 161-167
35. ∞ control for uncertain stochastic systems with state delay. IEEE Trans Automat Control 47 12 (2002) 2089-2094
36. ∞ model reduction of Markovian jump linear systems. Syst Control Lett 50 2 (2003) 103-118