Uncertain Stability And Robust Stabilization Of Fractional Singular Systems

Fractional order calculus is a generalization of the traditional integer order calculus,and can describe the behavior of many systems.The singular system is a kind of dynamic system that is more common than normal systems.Using generalized system to describe the algebraic relationship between state variables can be more accurate in many practical systems.The fractional order singular system which can be derived by mixing the two systems together is more complex,therefore,it received scholars' extensive attention at home and abroad.The main content of this article is as follows:Based on the stability criterion of the normal fractional order system,we study the admissibility of fractional order singular system.The sufficient and necessary conditions of the fractional order generalized autonomous system are given in the form of linear matrix inequalities.Compared with the criterion of literature[1],the number of variables in this paper is small and the form is more concise.Based on the stability condition of fractional order singular system,we study it's problem of state feedback control.The state feedback stabilization conditions are given in the form of linear matrix inequalities.This criterion is extend to the uncertain fractional order singular systems to get results that can broaden the scope of application.We can see the number of variables in this paper is small and the scope of application is larger though numerical examples.Based on the designing method of state feedback controller in this paper,we further study the problem of static output feedback control of fractional order singular system.After two steps of derivation,the control rate of static output feedback stabilization are given in the form of linear matrix inequalities.This criterion is extend to the uncertain fractional order singular systems to get results that can broaden the scope of application.The result of this paper has smaller number of variables and less matrix dimension compared with the conditions of theorem 14 of literature [2].The results obtained from the theorem of this paper has wider scope of application than theorem 2 of literature [3]does.Numerical examples illustrate the effectiveness and superiority of the results of this chapter.Finally,the conclusion of research is summarized,and the future work is pointed out.