Admissibility And Asymptotic Stability Of Fractional Order Singular Systems

In the past years,fractional calculus has been widely used in many fields,such as biomedical engineering,dielectric polarization,high-energy physics,viscoelasitc materi-als with memory and hereditary effects and so on.In addition,singular systems have attracted great widespread interest from many experts and scholars due to it given bet-ter description of physical systems.Therefore,it have great practical significance and broad application to studying fractional order singular systems.In this paper,accord-ing to a strict linear matrix inequality without equality and Lyapunov functional,the admissibility of Caputo fractional order singular systems and the asymptotic stability of Riemann-Liouville fractional order singular systems with multiple delays and nonlinear terms are discussed.The specific work in this paper is as follows:In the first chapter,we present the research background and main works in this paper.In the second chapter,we introduce the relevant knowledges about fractional calculus and the theory of singular systems,then the relevant definition and lemma in this paper are presented.In the third chapter,the necessary and sufficient conditions of admissibility for Ca-puto fractional order singular systems,uncertain Caputo fractional order singular systems and corresponding closed-loop systems are derived by constructing a strict linear matrix inequality without equality.In the fourth chapter,according to the revelent linear matrix inequality and matrix equation,two sufficient conditions of asymptotic stability for R.iemann-Liouville fractional order nonlinear singular systems with multiple delays are presented by constructing Lya-punov functional.Then,two numerical examples are presented to verify the feasibility of main results.