Static Output-Feedback Integral Sliding Mode for T-S Fuzzy Descriptor Systems with Partly Unmeasurable Premise Variables

This paper focuses on the problem of designing static output-feedback sliding mode controllers for T-S fuzzy descriptor systems with partly unmeasurable premise variables. A canonical form-based static output-feedback integral sliding mode controller design method is proposed, where only the measurable premise variables are used. Measurable premise variables and unmeasurable premise variables in the T-S fuzzy descriptor are separated. The designing matrix in the output-based integral-type switching function is solved by a canonical form-based method. Both the finite-time reachability of the sliding surface and the asymptotic stability of the resulting closed-loop system are proved. Finally, an example is given to illustrate the effectiveness of proposed method.

I. Introduction

The Takagi-Sugeno (T-S) fuzzy modelling method has been considered as one of the most effective modelling for nonlinear systems since it was proposed in [1]. The T-S fuzzy systems can be viewed as a series of local linear time-invariant systems connected by membership functions, which facilitates the extension from the linear control theory to the nonlinear systems. As the basis of nonlinear control problem, the T-S fuzzy modelling method has been widely studied from both theoretical and practical viewpoint [2], [3]. Moreover, the T-S fuzzy descriptor system is a fuzzy blending of a series of linear descriptor subsystems. Due to the existence of the derivative matrix, a wider range of nonlinear models can be modelled into T-S fuzzy descriptor systems [4]. Since the inception of T-S fuzzy descriptor systems, such modelling approach is widely applied in many fields [5]- [9]. According to the T-S fuzzy theory, the premise variable may depend on state, time or exogenous parameters. When the premise variable depends on accessible variables, it is called as the measurable premise variable. Similarly, an unmeasurable premise variable depends on inaccessible variables including unmeasurable system states or unknown parameters. In [10], a set-theoretic description was adopted to separate measurable premise variables and unmeasurable premise variables.