Robustness Analysis And H_∞Control For Time-varying Descriptor Systems

In this paper, the robustness analysis and H_∞control of time-varying descriptorsystems has been studied by using Lyapunov function theory and Riccati equation.Firstly, considering the time-varying general singular system, by using analysismethod of singular Lyapunov inequality and restrained equal transformation，the conceptof admissibility and quadratic admissibility for time-varying general singular system wasput forward, a Lyapunov inequality for time-varying general singular system is established,the problem of admissibility for time-varying general singular system is transformed intosolving the Lyapunov inequality problem. The necessary and sufficient conditions ofadmissibility and quadratic admissibility are obtained for the system.In addition, the problem of the robust stability with finite time domain and the designmethods of feedback controller for a class of time-varying descriptor systems withnonlinear disturbance is considered. The sufficient condition for finite time domain robuststability and the design methods of the robust stabilizing controller are presented base onthe Lyapunov function theory, Riccati equation and Q-norm. The close-loop system canrun normally in the time interval which the disturbance arise under this robust stabilizingcontroller. Finally, a numerical simulation shows the effectiveness of this approach.Finally, the problem H_∞control for time-varying descriptor system withnorm-bounded uncertainties in the system matrices is investigated. The admissibility andH_∞disturbance attenuation problem for the time-varying descriptor system withnorm-bounded uncertainties are analyzed by bounded real lemma. The H_∞problem for thetime-varying descriptor system is transformed to the time-invariant descriptor system byparameterized linear matrix inequality (LMI) and schur complement theory if uncertaintiessatisfy the norm-bounded condition. The result that the descriptor system withnorm-bounded uncertainties is equal to the time-invariant descriptor system is concluded.