Exponential $H_{\infty}$ Filtering for Singular Markovian Jump Systems With Mixed Mode-Dependent Time-Varying Delay

Abstract

This paper is concerned with the exponential <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm H}\infty$</tex></formula> filter design for a class of continuous-time singular Markovian jump systems with mixed mode-dependent time-varying delay. By constructing a new Lyapunov-Krasovskii functional and utilizing some advanced techniques, a less conservative delay-dependent bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs), which guarantees the considered system is exponentially admissible with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex> </formula> performance. Based on the BRL, the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$H_{\infty}$</tex></formula> filtering problem is solved and an explicit expression of the desired filter can be given. Two numerical examples are presented to illustrate the effectiveness and the potential of the proposed techniques.