Robust stability, stabilization and ℋ∞ control of time-delay systems with Markovian jump parameters

International Journal of Robust and Nonlinear Control

Volumn 13, Issue 8, 2003, Pages 755-784

  Mahmoud, Magdi S ^a   Shi, Peng ^b  

^a UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

^b DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION   (Australia)

Author keywords

state feedback; Markovian jump parameters; Stochastic stability; Time delay systems; Uncertain parameters

Indexed keywords

CONTROL SYSTEM SYNTHESIS; FEEDBACK CONTROL; MARKOV PROCESSES; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; RICCATI EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS); STATE FEEDBACK; STOCHASTIC CONTROL SYSTEMS; SYSTEM STABILITY; UNCERTAIN SYSTEMS;

MARKOVIAN JUMP PARAMETERS; STOCHASTIC STABILITY; UNCERTAIN PARAMETERS;

DELAY CONTROL SYSTEMS;

EID: 0037629903     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.744     Document Type: Article

References (24)

1. Elliott RJ, Sworder DD. Control of a hybrid conditionally linear Gaussian processes. Journal of Optimization Theory and Applications 1992, 74, 75-85.
2. Srichander R, Walker BK. Stochastic analysis for continuous-time fault-tolerant control systems. International Journal of Control 1989; 57(2)433-452.
3. Willsky AS. A survey of design methods for failure detection in dynamic systems. Automatica 1976; 12(5):601-611.
4. Dufour F, Bertrand P. The filtering problem for continuous-time linear systems with-Markovian switching coefficients. System and Control Letters 1994; 23(5):453-461.
5. Dufour F, Bertrand P. An image-based filter for discrete-time Markovian jump linear systems. Automatica 1996, 32(2):241-247.
6. Davis M. Markov Models and Optimization. Champman & Hall: London, 1992.
7. Ji Y, Chizeck HJ. Jump linear quadratic Gaussian control: steady-state solution and testable conditions. Control-Theory and Advanced Technology 1990; 6(3):289-319.
8. Morozan T. Stability and control for linear systems with jump Markov perturbations. Stochastic Analysis and Applications 1995; 13(1):91-110.
9. Krasovskii NN, Lidskii EA. Analysis design of controllers in systems with random attributes. Part I. Automation and Remote Control 1961; 22:1021-1025.
10. Sworder DD. Feedback control of a class of linear systems with jump parameters. IEEE Transactions on Automatic Control 1969; 14(1):9-14.
11. Kushner H. Stochastic Stability and Control. Academic: New York, 1967.
12. Fleming W, Sethi S, Soner M. An optimal stochastic production planning problem with randomly fluctuating demand. SIAM Journal of Control and Optimization 1987; 25:1494-1502.
13. Ji Y, Chizeck HJ, Controllability, stabilizability and continuous-time Markovian jump linear-quadratic control. IEEE Transactions on Automatic Control 1990; 35:777-788.
14. Feng X, Loparo KA, Ji Y, Chizeck HJ. Stochastic stability properties of jump linear systems. IEEE Transactions on Automatic Control 1992; 37(1):38-53.
15. Mahmoud MS. Robust Control and Filtering for Time-Delay Systems. Marcel-Dekker: New York, 1999.
16. Dorato P, Yedavalli RK. Recent Advances in Robust Control. IEEE Press: New York, 1990.
17. Shi P, Boukas EK, Agarwal RK. Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delays. IEEE Transactions on Automatic Control 1999; 44(1):2139-2144.
18. Shi P, Boukas EK, Agarwal RK. Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters. IEEE Transactions on Automatic Control 1999; 44(8):1592-1597.
19. ∞ control for linear systems with Markovian jumping parameters. Control-Theory and Advanced Technology 1993; 9(2):457-466.
20. ∞ control of jump linear systems with time-delay. International Journal of Control 2001, 74(4):329-340.
21. Mahmoud MS, Al-Muthairi NF. Design of robust controllers for time-delay systems. IEEE Transactions on Automatic Control 1994, 39(5):995-999.
22. Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in Control. SIAM Studies in Applied Mathematics: Philadelphia, 1994.
23. Gahinet P, Nemirovski A, Laub AL, Chilali M. LMI Control Toolbox. The Math Works, Inc.: Boston, MA, 1995.
24. ∞ control for Markovian jumping linear systems with parametric uncertainty. Journal of Optimization Theory and Applications 1997; 95(1):75-99.