Robust H_∞Control For Descriptor Systems With Time-delay

Descriptor system, which is more applied than normal systems, also is called singular systems. Descriptor systems theory developed rapidly since1970s, which has gradually developed from the basic direction to the deep direction. In recent years, more attention has been paid on uncertainty problem or time-delay problem of the singular large-scale system due to the wide application background. In this paper, the robust H∞control problem for the singular system with uncertain and time-delay is studied via linear matrix inequality (LMI) method and Lyapunov stability theory. The main results are described as follows:The robust H∞state feedback control problem for a class of nonlinear descriptor system with uncertainty and time-varying delay is studied, and the sufficient condition of the existence of state feedback controller is given, which makes the closed-loop system asymptotically stable and satisfies H∞norm constrain. The numerical example illustrates the effectiveness and correctness of the conclusion.The robust H∞performance for a class of Markovian jump system with uncertainty and time-delay is analyzed. The sufficient condition is given in terms of LMI, which makes the system robust-stochastically stable for all admissible uncertainties, then the sufficient condition that satisfies the robust H∞performance is obtained. At the same time, using the LIM toolbox in Matlab, numerical example is given to show the effectiveness and correctness of theorems.The robust H∞performance for a class of Markovian jump system with uncertainty and time-varying delay is considered. The sufficient condition that guarantees the system robust-stochastically stable for all admissible uncertainties and satisfies H∞performance is given. The numerical example illustrates the effectiveness and correctness of theorems.