Stability Analysis And Controller Design Of Several Generalized Systems

Singular system is a kind of dynamic system of more general form and abroad applied background,called descriptor systems,implicit systems and differential-algebraic systems also.For generalized system equation can be more accurate to describe some physical phenomena,it has been widely used in many practical control system.On the one hand,with the devel-opment of the economy and constant progress of science and technology,singular systems is increasingly applied to such as cross-linked systems,economic systems,electrical network and electric systems and so on,which has aroused research interests of many scholars both at home and abroad.On the other hand,application of singular systems in engineering system such as process of chemical technology,long distance transmission of pneumatic system received much concern over the past decade.The first chapter introduces development process,latest development and research of sin-gular delay systems,uncertain singular systems and fractional order singular systems(0<a<1)in detailed respectively after information research and book reading.Next it presents research contents,research methods adopted and meaning and purpose of research.The second chapter presents stability and stabilization criteria of continuous singular delay systems by strict linear matrix inequalities(LMIs).We present strict LMIs admissibility criteria including stability of singular delay systems.Two class of state feedback controllers are given to guarantee that the given singular delay system is admissible.In the considered LMIs criteria,only a positive definite matrix Q needed to solved without involving additional matrices.For this reason,the merit of obtained LMIs criteria is that they simplify and improve the existing results.Numerical examples are given to verify the effectiveness of the criteria.The third chapter considers the problems of robust stability analysis,robust controller de-sign and guaranteed cost controller design of singular systems with parameter uncertainty.Us-ing the method of constructing P matrix,variable quantity of strict linear matrices inequalities obtained is reduced.The concepts of generalized quadratic stability and generalized quadrat-ic stabilization implies robust stability and robust stabilization are given respectively.In the following,sufficient condition of generalized quadratic stability are presented by strict linear matrix inequality,then state feedback controller which guarantees generalized quadratic stabil-ity of closed uncertain singular is designed.And guaranteed cost controller is obtained,which make the closed uncertain singular stable and satisfying one cost function.At last,three exam-ples are given to verify the conditions obtained are feasible and valid.The fourth chapter discusses the problems of stability analysis and state feedback con-troller designing of fractional order singular systems with order ?:0<?<1.With construct-ing P matrix and Lyapunov direct methods,this chapter present sufficient admissibility linear matrix inequality condition which contain stability and stabilization of fractional order singular systems.The criterion simplify and improve the existed conclusion.Then this chapter give numerical examples to verify the effectiveness of the criteria.In the fifth chapter,inspired by novel lemma of stability of fractional order systems and approach of matrix transform,we study stability of fractional order singular systems further.The more simple and convenient stability criteria are obtained.But for the reason that available tool is absence,we can not design state feedback controller using this method.I believe this problem will give more power to do research.