Guaranteed-Cost Non-Fragile Robust H/spl infinity/ Control for a Class of Uncertain Singular Systems with Multiple Time Delays

Abstract

This paper considers the problem of non-fragile guaranteed-cost H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controller design method for uncertain singular systems with multiple time delays in state and control input. First, based on the stability criterion and linear matrix inequalities(LMIs), a sufficient condition of the existence of the non-fragile guaranteed-cost H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controller is established. Then the problem of control is solved via a robust controller with gain additive and multiplicative perturbations, the designed controller guarantees that the closed-loop system is regular, impulse free and asymptotically stable for all admissible uncertainties, and satisfies a cost bound, more over, also satisfies H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance index, which has better adaptability against variety of the environment parameter. A numerical example demonstrates that the systems are robust to both the uncertainty of parameters and perturbations of controller gain.