Region Stability Control For Singular Systems

Stability is the precondition in engineering practice of concrete systems. Region-stable systems usually possess many nice properties besides stable. For example, a system will have α-attenuation which will expedite the speed of convergence, if all the poles of a system are placed in D_α-region which D_α = {z ∈ C : Rez < -α}(α > 0). Therefore, the region-stability problem of systems has been an attractive issue for many researches. Into the bargain, there exist inevitably uncertainty for systems in practical industrial process control. One is in the coefficient of system, the other is in the coefficient of controller. the practical needs make it much more important to guarantee the systems suffered from disturbance of uncertainty to be region-stable and possess some dynamic performance. Moreover, a large number of industrial process can be modeled as time-delay systems because of kinds of delay phenomenon exist in practical industrial process and dominate the system's stability and other performance. Simultaneously, the H_∞ control theory which can solve the robust stability and disturbance remaining problem has been applied diffusely in control domain. The modus is to design dynamic compensator so as to retrain the disturbance of environment and guarantee the closed-loop system still to be stable. In addition, singular system can describe the physical speciality of many engineering practice well, such as electron network system, electric power system, economy system, mechanism system, chemic industrial system, missilery system, aeronautic system and so on. Thus the study of region stability and design of corresponding controller with H_∞, restrict are of importance value both in theory and practise.In this paper, we use the linear transformation, linear matrix inequality, Lyapunov function method, et al to do research on the region-stability and the corresponding control with perfomance limit.The main contents are as follows:1) The problem of robust H_∞ control with α-stability constraints is discussed for a class of delay singular systems with parametric uncertainties. The singular system...