Stability criteria for a class of nonlinear two-dimensional systems via the Takagi-Sugeno fuzzy model

Abstract

This paper is concerned with the problem of stability analysis of a class of nonlinear two-dimensional systems. The underlying nonlinear two-dimensional systems described by Roesser model are represented by the Takagi-Sugeno fuzzy model form. In the process of stability analysis, a parameter-dependent Lyapunov function and a approach of introducing additional matrix variable have been applied for achieving less conservative stability criteria for verifying the asymptotical stability of the underlying nonlinear Roesser-type discrete-time two-dimensional systems. Furthermore, the obtained stability criteria are formulated in the terms of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, some numerical results have been given to illustrate the effectiveness and applicability of the proposed approach.