Guaranteed Cost Control For Uncertain Singular Systems

In this paper, we study problems of the resilient guaranteed cost control for uncertain continuous singular systems, the guaranteed cost control with H_∞ and pole placement in a disk of discrete singular systems , and the guaranteed cost control of continuous singular systems with a time-multiplied linear quadratic cost function. For a physical system, the sources of uncertainties are various and the uncertainties always own different characters. With a appropriate equivalent transformation, these uncertainties could be shown as a diagonal construction, namely structured uncertainties. This kind of uncertainties can be regarded as an extension of the norm bounded ones, so the structures can be used to improve the designed method and reduce the constraint of the conclusion. If there is a time-multiplied gene in the quadratic cost function, it could help the state response approach zero more quickly, and shorten the stabilizing time of the systems. We also study several kinds of multi-objective guaranteed cost control in this paper. For example, based on the cost function required, other requests such as H_∞, pole placement in a disk and so on, all of which would make the systems possess better dynamic performances.The main content of this paper is as follows:In chapter 2, the resilient guaranteed cost control for singular systems with structured uncertainties is considered. Firstly, the sufficient condition in terms of LMIs for the existence of resilient guaranteed cost controllers is obtained for all the admissible uncertainties of systems and disturbances of controllers. Using the method of variable replacement to deal with the LMIs, we obtain the singular resilient dynamical output-feedback controllers. At last the numerical example is given to illustrate the designed method.Chapter 3 considers the guaranteed cost control for a class of norm bounded uncertain singular systems with a time-multiplied linear quadratic cost function, and...