Generalized System Of Passive Resistance

This paper studies the passivity problem for a class of continuous, time-invariant and linear singular systems. In recent years, Many scholars, by using linear matrix inequations gave some sufficient conditions under which ensure the systems are passive and allowable. When D is inverse, Xiuhua Zhang and Qingling Zhang give a necessary and sufficient condition for passivity of a class of continuous, time-invariant and linear systems by using the method of differential geometry. The study of passivity problem for a class of continuous, time-invariant and linear singular systems is continuing in this paper, i.e., the condition on the invertibility of D is weakened to D + DT≥0.In this preface, the importance of the study of sigular systems is first presented, Then the relation between passivity and positive real character, the relation between passivity and Lyaponov stabilizability, the relation between passivity and dissipation are given. And then, a summary of passivity and passive control (robust passive control) methods are given, respectively, in normal systems (nolinear system, uncertain linear system, delay linear system, and delay discrete-time system) and singular systems (linear singular system, delay linear singular system, discrete-time singular system, delay discrete-time singular system and uncertain discrete-time singular system). We compare those methods used to study passivity in the round.The main body of this paper is divided into three chapters: The first chapter gives a brief introduction to the development process of passivity and passive control problem. The present of passivity and passive control is divided up into three parts (linear normal systems, linear singular systems and delay linear singular systems). The results for passivity and passive control (robust passive control) in several kinds of linear systems are introduced which is important for us to comprehend the theory of passivity. The second chapter gives three theorems. A new necessary and sufficient condition of passivity is given under D + DT>0, and another necessary and sufficient condition of passivity is given under D + DT≥0. Theorems are proved by making use of differential geometry method, definition of passivity, and transformations of vectors and matrices. Chapter 3 presents two numerical examples which state the availability of Theorems, respectively.At last, it is pointed out that our method is different from those in the literature.