The Robust Stability And Stabilization Control Of Singular, Uncertain System With Delay

During the past years a great deal of interest has been denoted to the study of generalized systems and time-delayed systems due to their applications in representing and resolving problems concerning many naturally occuring systems, such as control systems, economic systems, management systems and so on.Consequently, we will meet some uncertain elements in practical control systems,for example, uncertain model paramenters, system perturbation, measure noises , external disturbance and so on.These are the source of causing instability in the world.In this paper, some new notions and design techniques are proposed for the systems with uncertainty in the light of rencent work in the theory of generalized systems, time-delayed systems, and that of robust stabilization. The main contents and results in this dissertation are as follows:1.The problems of robust stability for a type of singular interval systems with time-delay is studied. It gives us a sufficient condition for the stability of the system. While the definition of stability in the normal system has been extended to interval systems and obtained the stability by intesting a impositive matrix with three dimentions.2.For interval systems with delayed state, the H∞ control problem is investigated.The robust H∞ stabilization sufficient condition for the robust stabilization has been imposed. And given a robust H∞ controller by solving a certain algebraic Riccati inequality equation.While it has been extended quadratic stability and stabilization in the normal systems to the interval systems.3.The problems of robust stabilization and robust H∞ control for uncertain degeneratide systems with time-varying delay are studied,respectively.The problem addressed is the design of state feedback controllers such that the resulting closed-loop system is regular,impulse, stable while satisfying H∞ norm constraint. On disturbance attenuation for all admissible uncertainties. From the previous discussion,it is obvious that delays is the clue of this paper, which reflects the feature of functional differential equations.