On stability and stabilizability of singular stochastic systems with delays. (English) Zbl 1101.93077

Boukas, E. K.; Xu, S.; Lam, J.

J. Optim. Theory Appl. 127, No. 2, 249-262 (2005).

The paper deal with the problems of stability analysis and stabilization for singular Markovian jump system with time delays. Based on a set of linear matrix inequalities, the sufficient conditions which guarantee the regularity, absence of impulses, and stochastic stability of such systems are presented. Based on this, the sufficient conditions for the existence of a state feedback controller are derived. A memoryless controller is used in the paper and a design algorithm in terms of the solutions to linear matrix inequalities is proposed to synthesize the controller gains. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Reviewer: Tzvetan Semerdjiev (Sofia)

MSC:

93E15	Stochastic stability in control theory
93D15	Stabilization of systems by feedback

Keywords:

stochastic stability; stabilization of systems with feedback; singular systems; jump linear systems; linear matrix inequalities

References:

[3]	Lewis, F. L., A Survey of Linear Singular Systems, Circuits, Systems, and Signal Processing, Vol. 5, pp. 3–36, 1986. · Zbl 0613.93029
[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.
[22]	De Souza, C. E., and Fragoso, M. D., Robust HFiltering for Markovian Jump Linear Systems, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, pp. 4808–4813, 1996.
[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.