Proportional Observer design based on [formula omitted]-stability and Finsler's Lemma for Takagi-Sugeno systems

Abstract

This paper concerns Proportional Observer design for Takagi-Sugeno (TS) systems with Immeasurable Premise Variables using D-stability constraints and L2-gain analysis. The D-stability is used to control the dynamics of the designed observer (eigenvalues clustering in a prescribed Linear Matrix Inequality region) while the L2 technique minimizes the effect of Immeasurable Premise Variables on the state estimation error. In addition, Finsler's Lemma provides more flexibility and extra degrees of freedom through slack variables to obtain relaxed stability conditions. Numerical examples are presented to illustrate the effectiveness of the proposed approaches.