Robust H<inf>¿</inf> Reliable Control with Exponential Stabilization for Uncertain Delay Systems against Actuator Failure

Abstract

The problem of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> reliable control with exponential stabilization is investigated for time-varying delayed uncertain systems against actuator failure. By means of model transformation, the robust reliable exponential stabilization problem is reduced to an equivalent robust reliable stabilization problem. Based on Lyapunov stability theory, a sufficient condition of the existing of robust reliable controller with exponential stability is given. At the same time, another sufficient condition of the existing of robust reliable controller possessing H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index is presented. Those conditions are transformed to two linear matrix inequalities (LMIs). The resulting control systems retain robust reliable exponential stability and disturbance attenuation with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm bounds despite any outages within a prespecified subset of actuators.