Delay-dependent fuzzy static output feedback control for discrete-time fuzzy stochastic systems with distributed time-varying delays

Abstract

This paper is concerned with the delay-dependent H∞ fuzzy static output feedback control scheme for discrete-time Takagi–Sugeno (T–S) fuzzy stochastic systems with distributed time-varying delays. To begin with, the T–S fuzzy stochastic system is transformed to an equivalent switching fuzzy stochastic system. Then, based on novel matrix decoupling technique, improved free-weighting matrix technique and piecewise Lyapunov–Krasovskii function (PLKF), a new delay-dependent H∞ fuzzy static output feedback controller design approach is first derived for the switching fuzzy stochastic system. Some drawbacks existing in the previous papers such as matrix equalities constraint, coordinate transformation, the same output matrices, diagonal structure constraint on Lyapunov matrices and BMI problem have been eliminated. Since only a set of LMIs is involved, the controller parameters can be solved directly by the Matlab LMI toolbox. Finally, two examples are provided to illustrate the validity of the proposed method.