Brief paper: A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances

Authors:
Zidong Wang;Yurong Liu;Guoliang Wei;Xiaohui Liu
Affiliations:
Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK and School of Information Science and Technology, Donghua University, Shanghai 200051, China;Department of Mathematics, Yangzhou University, Yangzhou 225002, China;School of Information Science and Technology, Donghua University, Shanghai 200051, China;Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

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.