Delay-dependent H-infinity control for linear descriptor systems with delay in state

Abstract

A delay-dependent H-infinity control for descriptor systems with a state-delay is investigated. The purpose of the problem is to design a linear memoryless state-feedback controller such that the resulting closed-loop system is regular, impulse free and stable with an H-infinity norm bound. Firstly, a delay-dependent bounded real lemma(BRL) of the time-delay descriptor systems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor model transformation of the system and by taking a new Lyapunov-Krasovsii functional. The introduced functional does not require bounding for cross terms, so it has less conservation.Secondly, with the help of the obtained bounded real lemma, a sufficient condition for the existence of a new delay-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrix inequalities and the solvability of the problem can be obtained by using an iterative algorithm involving convex optimization. Finally, numerical examples are given to demonstrate the effectiveness of the new method presented.