On stability and stabilizability of singular stochastic systems with delays

Journal of Optimization Theory and Applications

Volumn 127, Issue 2, 2005, Pages 249-262

  Boukas, E K ^a   Xu, S ^b   Lam, J ^c  

^a GERAD   (Canada)

^b NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Jump linear systems; Linear matrix inequalities; Singular systems; State feedback; Stochastic stability; Stochastic stabilizability

Indexed keywords

CONTINUOUS TIME SYSTEMS; LINEAR MATRIX INEQUALITIES; LINEAR SYSTEMS; MARKOV PROCESSES; STOCHASTIC SYSTEMS; SYSTEM STABILITY;

CONTINOUS TIME; JUMP LINEAR SYSTEM; LINEAR MATRIX IN EQUALITIES; MARKOVIAN JUMP PARAMETERS; SINGULAR LINEAR SYSTEMS; SINGULAR SYSTEM; STABILIZABILITY; STOCHASTIC STABILITY; STOCHASTIC STABILIZABILITY; SYSTEMS WITH DELAYS;

STATE FEEDBACK;

EID: 28244459610     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-005-6538-5     Document Type: Article

References (27)

1. DAI, L., Singular Control Systems, Lecture Notes in Control and Information Sciences, Springer Verlag, New York, NY, Vol. 118, 1989.
2. KUMAR, A., and DAOUTIDIS, P., Feedback Control of Nonlinear Differential-Algebraic Equation Systems, AIChE Journal, Vol. 41, pp. 619-636, 1995.
3. LEWIS, F. L., A Survey of Linear Singular Systems, Circuits, Systems, and Signal Processing, Vol. 5, pp. 3-36, 1986.
4. NEWCOMB, R. W., The Semistate Description of Nonlinear Time-Variable Circuits, IEEE Transactions on Circuits and Systems, Vol. 28, pp. 62-71, 1981.
5. FRIDMAN, E., A Lyapunov-Based Approach to Stability of Descriptor Systems with Delay, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, pp. 2850-2855, 2001.
6. LAN, W., and HUANG, J., Semiglobal Stabilization and Output Regulation of Singular Linear Systems with Input Saturation, IEEE Transactions on Automatic Control, Vol. 48, pp. 1274-1280, 2003.
7. XU, S., DOOREN, P. V., STEFAN, R., and LAM, J., Robust Stability and Stabilization of Discrete-Time Singular Systems with State Delay and Parameter Uncertainty, IEEE Transactions on Automatic Control, Vol. 47, pp. 1122-1128, 2002.
8. XU, S., and LAM, J., Robust Stability and Stabilization of Discrete-Time Singular Systems: An Equivalent Characterization, IEEE Transactions on Automatic Control, Vol. 49, pp. 568-574, 2004.
9. XU, S., and YANG, C., Stabilization of Discrete-Time Singular Systems: A Matrix Inequalities Approach, Automatica, Vol. 35, pp. 1613-1617, 1999.
10. FLETCHER, L. R., Pole Assignment and Controllability Subspaces in Descriptor Systems, International Journal of Control, Vol. 66, pp. 677-709, 1997.
11. TAKABA, K., MORIHIRA, N., and KATAYAMA, T., A Generalized Lyapunov Theorem for Descriptor Systems, Systems and Control Letters, Vol. 24, pp. 49-51, 1995.
12. VERGHESE, G. C., LEVY, B. C., and KAILATH, T., A Generalized State Space for Singular Systems, IEEE Transactions on Automatic Control, Vol. 26, pp. 811-831, 1981.
13. XU, S., LAM, J., and ZHANG, L., Robust D-Stability Analysis for Uncertain Discrete Singular Systems with State Delay, IEEE Transactions on Circuits and Systems I, Vol. 49, pp. 551-555, 2002.
14. XU, S., and LAM, J., Robust Stability for Uncertain Discrete Singular Systems with State Delay, Asian Journal of Control, Vol. 5, pp. 399-405, 2003.
15. BOUKAS, E. K., and LIU, Z. K., Deterministic and Stochastic Systems with Time Delay, Birkhauser, Boston, Massachussetts, 2002.
16. MARITON, M., Control of Nonlinear Systems with Markovian Parameter Changes, IEEE Transactions on Automatic Control, Vol. 36, pp. 233-238, 1991.
17. BOUKAS, E. K., and HANG, H., Exponential Stability of Stochastic Systems with Markovian Jumping Parameters, Automatica, Vol. 35, pp. 1437-1441, 1999.
18. BOUKAS, E. K., and LIU, Z. K., Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays, Journal of Optimization Theory and Applications, Vol. 109, pp. 587-600, 2001.
19. FENG, X., LOPARO, K. A., JI, Y., and CHIZECK, H. J., Stochastic Stability Properties of Jump Linear Systems, IEEE Transactions on Automatic Control, Vol. 37, pp. 38-53, 1992.
20. JI, Y., and CHIZECK, H. J., Controllability, Stabilizability, and Continuous-Time Markovian Jump Linear Quadratic Control, IEEE Transactions on Automatic Control, Vol. 35, pp. 777-788, 1990.
21. MAO, X., Stability of Stochastic Differential Equations with Markovian Switching, Stochastic Processes and Their Applications, Vol. 79, pp. 45-67, 1999.
22. ∞ Filtering for Markovian Jump Linear Systems, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, pp. 4808-4813, 1996.
23. ∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty, Journal of Optimization Theory and Applications, Vol. 95, pp. 75-99, 1997.
24. ∞ Control of Uncertain Markovian Jump Systems with Time Delay, IEEE Transactions on Automatic Control, Vol. 45, pp. 77-83, 2000.
25. ∞ Control of Discrete-Time Markovian Jump Linear Systems with Mode-Dependent Time Delays, IEEE Transactions on Automatic Control, Vol. 46, pp. 1918-1924, 2001.
26. ∞ Control of Jump Linear Systems with Time Delay, International Journal of Control, Vol. 74, pp. 329-340, 2001.
27. JUNE, F., SHUQIAN, Z., and ZHAOLIN, C., Guaranteed Cost Control of Linear Uncertain Singular Time-Delay Systems, Proceedings of the 41th IEEE Conference on Decision and Control, Las Vegas, Nevada, pp. 1802-1807, 2002.