Non-fragile Control For Singular Linear Systems

Many practical processes can be modeled as singular systems, such as constrained control problems, electrical circuits, certain population growth models and singular perturbations. In the past several decades, stability and control problems of singular systems have been extensively studied due to the fact that the singular system better describes physical systems than the normal systems. Compared with normal systems, the singular system has a more complicated yet richer structure. Considering the effect of time delay and uncertainty on the dynamical performance of the systems, robust stability and control problems have been more recently investigated for the uncertain singular systems with time delay. However, most results are under the assumption that the designed controller can be exactly implemented. When the controller can't be exactly implemented, we should design non-fragile controller for uncertain singular systems, this is the main content of this paper, specifically as follows:We deal with the design problem of robust and non-fragile state feedback controller for a class of uncertain singular linear system with state delay. One class of perturbation is considered, namely, additive. Design of the state feedback non-fragile controller for H_∞control under the class of gain perturbation is given in terms of linear matrix inequalities. The designed controller can guarantee the closed-loop system is regular, stable and impulse free as well as has of a H_∞norm bound.This paper deals with the design of delay-dependent robust and non-fragile H∞state feedback controller for a class of singular linear system with time-varying delay. Less limitation for the derivative of time-delay, using the Schur complement lemma and transformed variables, found a suitable Lyapunov function, the obtained sufficient condition can be written in a LMI form. The designed controllers can guarantee that the closed-loop system is regular, stable, impulse free and disturbance attenuation in spite of controller gain variations.