Controller Synthesis for T-S Fuzzy Systems Based on Premise Variable-Dependent $H_{\infty}$ Performance

This paper tackles the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> control problem for T-S fuzzy systems. For a class of systems whose premise variables often work in some fuzzy sets frequently, by combining some properties of the product inference engine and set theory, a premise variable-dependent <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> index is proposed. And the developed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> controller can guarantee better disturbance attenuation ability under fuzzy rules where the system often works. Sufficient conditions for solving the feedback gain matrix are expressed as linear matrix inequalities (LMIs). Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.