Stability And Passive Control Of Singular Systems

Singular system has a broad range of applications background, and can better describe the actual system, so the past three decades has attracted a large number of experts and the attention of scholars has made some valuable conclusions, it is becoming a hot research topic of modern control theory . The diffusion theory is playing the important role in the system investigation into stability. Not only passivity is a principal aspect in the diffusion, but also is one kind of higher level abstract of stability. This paper concerns the passive control problem of singular systems in the light of uncertainty; also it discusses the passive control problem of the nonlinear bilinear system. The main contents and results in this dissertation are as follows:In Chapter 2, the problems of passive control for linear systems with time-varying delay in the states and parameter uncertainty. Through the linear time-varying delay singular systems with no parameter uncertainty, we solved the passive control problem of the system which contains parameter uncertainty, and obtained a linear state feedback controller such that the system is passivity.In Chapter 3, the problem of robust passive control are addressed for uncertain discrete-time singular systems. Using the method of generalized Lyapunov function and strict linear matrix inequality, a sufficient condition is presented for the system to be generalized quadratically stable and strictly passive.Finally, for bilinear singular systems with time-delay, the passive control problems are investigated. By means of linear matrix inequalities and generalized algebra Ricatti inequalities, a sufficient condition is derived such that a prescribed bilinear singular system is asymptotically stable and strictly passive.