Research On Proportional-plus-derivative Feedback Guaranteed Cost Control Of Descriptor Systems

In actual descriptor systems, the impulse modes usually cause instability especially for the uncertain descriptor systems. So, the problem of elimination of impulse modes must be considered.It is different to just use proportional state feedback to eliminate the impulses for the impulse incontrollable descriptor systems.For that, it is necessary to use derivative feedback to eliminate impulses. Although derivative feedback can alter the dynamic orders and influence the characters of the systems ultimately, the derivative feedback can't always improve the systems more than the proportional feedback. Actually, the proportional feedback and the derivative feedback have their respective advantages based on the different structure.That display the advantages of the proportional-plus-derivative feedback.In this dissertation, the discussions about the problems of the design of proportional-plus-derivative feedback controller for descriptor systems are stressed. The main results in this dissertation are as follows.(1)The problems of impulse removing and poles placement are investigated for descriptor systems under proportional-plus-derivative feedback control.A necessary and sufficient condition which is to keep the plant regular, impulse-free, and stable is obtained by using proportional-plus-derivative feedback control and a necessary and sufficient condition which is to keep poles placement arbitrary is also obtained. At last, a numerical example is given to illustrate the methods.(2)The problem of linear-quadratic optimal control of descriptor systems has been dealt with in the paper. The problem has been discussed with a quadratic cost index which has derivative of the states. A sufficient condition is given and the result is expressed as proportional-plus-derivative feedback control.(3)The problem of guaranteed cost control for the uncertain descriptor systems has been discussed. The problem of guaranteed cost control was dealt with for a class of uncertain descriptor systems, whose class is with parameter uncertainties and norm-bounded. And with a quadratic cost index which has derivative of the states. The purpose of the problem was to design a Proportional-plus-derivative State Feedback controller such that, for all admissible uncertainties, the closed-loop descriptor systems keep normalization and robust stabilization, at the same time an adequate level of a quadratic cost index can be guaranteed. At last, a numerical example is given to illustrate the methods.(4)The problem of non-fragile guaranteed cost control for uncertain descriptor systems is introduced in the paper. Discusses the design problem of non-fragile guaranteed cost controller for a class of linear descriptor systems with structural uncertainties.A linear quadratic cost index which has derivative of the states is considered as a performance measure.We discuss the existence of the non-fragile guaranteed cost controllers in cases of both additive and multiplicative perturbation based on discussing the augmented systems by using Lyapunov theory and linear matrix inequality method. The controller guarantees the robust stability of the closed-loop systems and an adequate level of a quadratic cost index. At last, a numerical example for both cases is given to illustrate the effectiveness of the theory.