Singular Systems With Delay-dependent Robust Stabilization And H ¡Þ Control

Descriptor systems, also are called singular systems, have more extensive application than normal systems. Time-delay systems' change rate of current state not only depends on the current state, but also depends on the past state. Descriptor time-delay systems are descriptor systems with time-delay, which have general sense in the research of descriptor time-delay system.This dissertation provides a study on descriptor time-delay systems by employing the improved free weighting matrix. The delay-dependent results are described by a matrix inequality with less conservative, and take off a mass of redundant varieties.For linear descriptor systems with time-varying delays, a sufficient condition is obtained which makes the system asymptotically stable, delay-dependent. Based on the condition, delay-dependent/rate dependent robust stabilization controller and delay-dependent robust H_∞controller are designed. Combining improved free weighting matrix method with varieties separation, a delay-dependent robust stabilization condition with less conservative is obtained, and new matrices decomposition algorithm is introduced based on iterative method. Simulation results are given to demonstrate that the new algorithm is less conservative. The results are extended to the systems with structure uncertainties and value bounded uncertainties.For a system with two time delays, delay-dependent criterias are derived by taking the relationship between the delays into account in the free weighting matrix method. The results are extended to the robust stabilization, robust H_∞control problem. In addition, the idea is extended to the derivation of delay dependent stability criteria for a system with multiple time delays. Simulation results demonstrate the improved free weighting matrix method is less conservative under the condition of multiple time delay.