On stability and stabilisation for uncertain stochastic systems with time-delay and actuator saturation

Abstract

This article concerns the stability analysis and design for uncertain stochastic systems with time-varying delays in state and actuator saturation. The parameter uncertainties belong to a convex polytopic set, and the delays are time varying. A sufficient condition is obtained in terms of a priori designed feedback matrix for determining if a given set is in inside the domain of attraction. Using the linear matrix inequality (LMI) approach, an estimate of the domain of attraction is presented. The problem of designing a state feedback controller such that the domain of attraction is enlarged is formulated through solving an optimisation problem with LMI constraints. A numerical example is given to illustrate the effectiveness of the proposed results.

Keywords:

• stochastic systems
• time-delay
• actuator saturation
• domain of attraction
• linear matrix inequality

Acknowledgement

This work is supported by The National Creative Research Groups Science Foundation of China (NCRGSFC: 60721062), The National High Technology Research and Development Program of China (863Program 2006AA04 Z182) and National Natural Science Foundation of P.R. China (NSFC: 60736021).