LMI Solution for Robust Static Output Feedback Control of Discrete Takagi–Sugeno Fuzzy Models

Abstract

This paper deals with the stabilization problem of discrete-time Takagi-Sugeno (T-S) fuzzy systems via static output controller (SOFC). The proposed method uses the descriptor approach to study this problem and leads to strict linear matrix inequality ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LMI</i> ) formulation. In contrast with the existing results, the method allows coping with multiple output matrices, as well as uncertainties. Moreover, the new proposed method can lead to less conservative results by introducing slack variables and considering multiple Lyapunov matrices. A robust SOFC for uncertain T-S fuzzy models is also derived in strict <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LMI</i> terms. Numerical examples are given to illustrate the effectiveness of the proposed design results.