Admissibility Analysis Of Continuous Singular Time-Delay Systems

In the 1970s,singular system theory was proposed.Singular systems can better describe the physical systems than regular ones and have been more extensively used.The problem of admissibility of singular system has been a hot topic in the field of control.Delay extensively exists in various systems such as network control systems,mechanical transmission systems and economic systems.The existence of delay affects dynamic performance of system and often leads to poor performance of system.The study of stability of time-delay systems has been attracting attention of scholars in the field of control both at home and abroad.For study of admissibility of continuous singular time-delay systems,regularity and impulse-free properties are guaranteed at first,then,stability of systems is considered.The study of admissibility of singular time-delay systems has important theoretical and practical value.Although some achievements have been made in the study of admissibility of singular time-delay systems,there still are space to be improved and developed.And many problems are still to be solved.Based on previous work,by the second method of Lyapunov stability,constructing the new Lyapunov-Krasovskii functionals(abbreviated as L-K functionals),in view of Bessel-Legendre inequality(abbreviated as B-L inequality),the problem of admissibility of continuous singular time-delay systems is addressed in this paper.The proposed results of admissibility conditions are obtained in terms of strict linear matrix inequalities,which are less conservative and superior to some research results both at home and abroad.The main work is as follows:(1)The problem of admissibility of continuous singular time-delay systems is studied.At first,a new augmented L-K functional is established.Then,third-order B-L inequality and fourth-order B-L integral inequality are applied to deal with some integral terms caused by derivation on L-K functional.Thus,an admissibility condition of continuous singular time-delay systems is obtained in terms of linear matrix inequality.B-L integral inequality is closer to truth value of some integral terms compared with Wirtinger inequality,the auxiliary function inequality and some other inequalities.Therefore,a less conservative admissibility condition of continuous singular time-delay systems is obtained.(2)Furthermore,the problem of admissibility of continuous singular time-delay systems is studied again.Constructing augmented L-K functional,relaxed L-K functional and triple integral L-K functional,and applying third-order B-L inequality,fourth-order B-L integral inequality and double B-L integral inequality to the integralterms caused by derivation on L-K functional,a less conservative admissibility condition of continuous singular time-delay systems is obtained,which is expressed in terms of linear matrix inequalityIn this paper,two admissibility conditions of continuous singular time-delay systems are obtained respectively.The two admissibility conditions are less conservative owing to the fact that some integral terms caused by derivation on L-K functional are enlarged less by B-L inequality compared with Jensen inequality,Wirtinger inequality,auxiliary function inequality and some other inequalities.To apply B-L inequality to deal with the integral terms,the augmented L-K functional is constructed.