Stochastic Stability Analysis and Fuzzy Linear Control of Stochastic Nonlinear Time-Delay Systems

Authors:	Karimi Hamidreza, University of Tehran, Iran (Islamic Republic of) Moshiri Behzad, University of Tehran, Iran (Islamic Republic of) Lucas Caro, University of Tehran, Iran (Islamic Republic of)
Topic:	1.4 Stochastic Systems
Session:	Control of Stochastic Systems
Keywords:	Fuzzy linear control; Linear matrix inequality; Time-delay systems; Stochastic systems; Exponential stability

Abstract

This paper presents the fuzzy linear control design method for a class of stochastic nonlinear time-delay systems with state feedback. First, the Takagi and Sugeno fuzzy linear model is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy linear controller is developed to stabilize the nonlinear system. The control law is obtained to ensure stochastically exponentially stability in the mean square, independent of the time-delay. The sufficient conditions for the existence of such a control are proposed in terms of certain linear matrix inequality. Finally, a simulation example is given to illustrate the applicability of the proposed design method.