Admissibility Analysis And Stability Control Of Several Singular Time-delay Systems

The science and technology have developing with high speed that made the com-plexity of modern control systems higher and higher.That made the previous simple sys-tems and research methods can no longer meet the requirements of complicated control.Therefore,it has become one of the majority of scholars to discover research methods that can fit complicated systems.For the reasons of complexity of singular system,and can description of singular systems more specifically.Therefor,the application of singular systems in complicated industrial systems has also attracted the attention of scholars.In this paper,the admissibility analysis of generalized time-delay sampling data systems is studied.The researches content of this paper are as follows:The stability of sampled data systems with time delays is discussed.The specific method is to use the time-delay partition method and the free matrix integral inequal-ity method to process the first-order integral term which contained in the derivation of Lyapunov functionals(LKFs).Then,the first-order integral term is transformed into an algebraic form,and a stable criterion is obtained.This method effectively reduced the conservativeness of the system.In this paper,the linear matrix inequality method is used to obtain sufficient conditions for system stability under the condition of known state feedback controller gain K.Then,assuming that the state gain matrix is unknown,the controller of the systems can be obtained by linear matrix inequality,Schur complement and convex combination technique.Furthermore,a sufficient condition for the stabil-ity of the system can be obtained.Later,we use two numerical examples to verify the effectiveness of the proposed stability criterion.The asymptotic stability of the T-S fuzzy sampling time-delay system is discussed.The peculiarity to approach nonlinear system of T-S fuzzy model is applied to dispose the nonlinear problem in the sampling time-delay system.The time-delay partition method and the free matrix integral inequality method are applied to dispose the integral term with time delay in the Lyapunov functional derivation.Combine Schur complement and convex combination technique obtains the conditions for the asymptotic stability of the system.And according to the piecewise linearized membership function method,a low conservative criterion is obtained.A simulation example shows the effectiveness of the proposed method.The problems of admissibility and state feedback stabilization of discrete-time singu-lar systems with time-varying delays are studied.The specific method is to equivalently transform the system into a new comparison form through decomposition.By taking ad-vantage of the Seuret summation inequality,the reciprocal convex inequality and some relaxation techniques,a criterion to ensure the admissibility of the related system depen-dent on delay is established.In addition,the problem of robustness and admissibility of uncertain systems is studied.A new admissibility condition is proposed.If the param-eter ? is prescribed,the admissibilization condition is linear matrix inequalities(LMIs).For more auxiliary matrices are added to the judgment condition,the dependence on the parameter ? is reduced,and the conservativeness is obviously reduced.Finally,two sim-ulation example shows the effectiveness of the proposed method.