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

作者：Wang, Zidong; Liu, Yurong; Wei, Guoliang^*; Liu, Xiaohui

来源：Automatica, 2010, 46(3): 543-548.

DOI：10.1016/j.automatica.2009.11.020

• Discrete-time nonlinear stochastic system
• Mixed time delays
• Lyapunov-Krasovskii functional
• Linear matrix inequality

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.

• 出版日期2010-3
• 单位东华大学; 扬州大学