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Zbl 1194.93134
Wang, Zidong; Liu, Yurong; Wei, Guoliang; Liu, Xiaohui
A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances. (English)
[J] Automatica 46, No. 3, 543-548 (2010). ISSN 0005-1098

Summary: This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.

MSC 2000:: *93C55 Discrete-time control systems
93E15 Stochastic stability

Keywords: discrete-time nonlinear stochastic system; mixed time delays; Lyapunov-Krasovskii functional; linear matrix inequality

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