Guaranteed Cost Control For Interval Discrete Time Singular Systems

In recent years, the guaranteed cost control for singular systems has attracted a lot of attention, and some significant results have been obtained. But the problems of the guaranteed cost control for uncertain discrete time singular systems are less discussed in some literatures and it is in primary developing stage. The guaranteed cost control for interval discrete time singular systems is discussed using the method of linear matrix inequality (LMI) in the thesis. The so-called interval system is that uncertainty can be described as each element of the parameter matrix is vary in prescribed rang. The main contents may be summarized as follows:(1) The main background of the problem discussed is introduced. Firstly, the background of guaranteed cost control for uncertain discrete systems is introduced, and a brief introduction to guaranteed cost control for descriptor systems is given. Secondly, some actuality of guaranteed cost control for interval discrete time singular systems is introduced. Finally, the main work is summarized.(2) The preparation knowledge is introduced and some knowledge on LMI and LMI toolbox and matrix inequalities common used in the thesis are summarized.(3) The problem of guaranteed cost control for interval discrete time singular systems is considered. A kind of equivalent description of the interval discrete-time singular systems is given, then using the method of LMI, a sufficient condition for solvability of the problem is obtained.(4) The problem of the H∞guaranteed cost control for interval discrete time singular systems is investigated. A sufficient condition for the solvability of the problem and the explicit expression of state feedback H∞guaranteed cost controller are obtained in terms of matrix inequalities. The controller is then designed to guarantee that the closed-loop systems is regular, causal, stable and satisfying a prescribed H∞norm bounded constraint, the cost function have a upper boundary for all admissible uncertainties.(5) The problem of resilient guaranteed cost control for a class of discrete time singular interval systems is discussed. Guaranteed cost control is considered under the elements in system matrix and input matrix are uncertain but vary in prescribed range and the controller with additive and multiplicative perturbations namely. And the controller can be obtained by solving a set of LMI.