Robust H<inf>∞</inf> reliable control for uncertain time varying delay systems by static output feedback

Abstract

The problem of robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> reliable control is investigated for time-varying delayed uncertain systems against actuator failure by means of static output feedback. In the considered systems, the parameters uncertainties satisfy generalized matching conditions, and the time-varying delay is bounded while its derivative is unrestricted. All the output of the actuator failures is assumed to be zero. Based on Lyapunov-Razumkhin stability theory, a sufficient condition of the existing of robust reliable controller possessing H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance index is given. At the same time, the designing approach of static output-feedback controller is presented. Those results are represented by linear matrix inequalities (LMIs) and are correlative with time delay. The resultant control systems retain asymptotic stability and disturbance attenuation with H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -norm bounds despite any outages within a prespecified subset of actuators. A numerical example shows the validity of the proposed design method.