Research On The Problem Of The Admissibility For Neutral Singular Systems With Time Delay

Neutral singular time-delay systems with time-delay information,neutral-and singularcharacteristics are a kind of complex time-delay systems.Compared with normal neutral delay systms and singular delay system,they are more general at the level of model stru cture and can describe many practical systems effectively such as powers systems and economic systems.Therefore,it has been widely concerned by scholars at home and abroad.Time delays are common in various practical systems,which often bring adverse effectw to the system,such as the instability and the performance degradation of systms.In order to avoid the adverse effects of time delay,it is necessary to study the influence of time delay on dynamic system.Therefore,it is of great theoretical significance and engineering value to analyze and study the neutral singular time-delay systems,which has a wide application prospect.In this paper,based on the Lyapunov-Krasovskii(L-K)functional theory,state decomposition method,integral inequality method and free weight matrix technology,the problems of admissibility analysis and state feedback control design of neutral singular time-delay systems are studied in detail by analyzing and improving the existing methods and conclusions.The main results are summarized as follows:1.The admissibility of neutral singular systems with mixed time-delays is researched.Firstly,considering the wholeness of neutral singular operators,the L-K functionals with simple forms are constructed.Secondly,by means of Newton-Leibniz formula,some zero equations are established.Combined with the free weight matrix inequality technique,the regularity and non-impulsivene ss of the system is discussed.The stability of the system is strictly analyzed and proved.The admissibility criteria based on strict linear matrix inequality conditionss are obtained,which reduce the complexity of calculation and decrease the conservatism of results obtained.Finally,three numerical examples are given to verify the effectiveness and low conservation of the theoretical results.2.The admissibility analys is of neutral singular time-delay systems based on the state decomposition method is studied.Firstly,considering the neutral and singular characteristics of the sytems and using the tate decomposition method,the system is decomposed into two parts,that is,the equivalent structural model composed of two subsystems is obtained.Secondly,by using the mixed time-delay information,the state decomposition augmented L-K functional is constructed.By using the integral inequality method,the free-weight m.atrix technique and the zero value equation approach,the regularity and non-impulsiveness of the system is fully discussed,and the delay dependent admissibility criterion is obtained.In addition,the case of neutral delay and discrete delay being the same is discussed.Finally,numerical examples and simulations show the effectiveness and feasibility of the proposed method.3.The exponential admissibility.of neutral systems with mixed time-varying delays is revised.Firstly,with full consideration of neutral and discrete time-delay informationr the equivalent structural model is established by using the state decomposition method.Secondly,the state decomposition augmented L-K functional containing the non-integral terms and integral terms is constructed.The integral inequality is used to estimate the L-K functional derivatives.By using,the free weight matrix and the zero-value equation technology,the regularity and non-impulsiveness of the systems are analyzed reasonably,and the delay dependent and delay decay rate dependent exponential admissibility criteria are obtained.In addition,it is discussed that neutral time-varying delay is equivalent to discrete time-varying delay.Finally,the validity of the theoretical results is verified by three numerical examples and simulations.4.The stochastic admissibility analysis and the design of state feedback controller for a class of neutral singular Markovian jump systems are studied.Firstly,considering the wholeness of the neutral singular operator,the neutral matrix conditions are relaxed and the modal-dependent augmented L-K functional is established.By using integral inequality,free-weight matrix method and zero-value equationtechnique,some sufficient modal dependent and delay dependent conditions are obtained,which can ensure that the system studied is regular,impulse free and stochastically stable.Secondly,the modal dependent state feedback cuntroller is designed and the corresponding closed loop system is established.The modal dependent and delay dependent stochastic admissibility criterion is obtained.Thirdly,by means of singular value decomposition,the admissibility sufficient condition based on state feedback controller design is transformed into a sufficient condition based on strict lineax matrix inequality:And the corresponding state feedback control parameters are derived.Firstly,the effectiveness of the proposed method is verified by numerical examples and simulations.5.The mean-square exponential admissibility analysis and the design of state feedback controller for neutral singular Markovian jump systems with mixed time-varying delayg are studied.Firstly,the equivalent structure modal is established by state decomposition method.On this basis,the regularity and non-impulsiveness of the systems are fully considered and the state decomposition augmented L-K functional of modal dependence is established.Secondly,the mean square exponential admissibility criterion related to model-dependence,mixed delay-dependence and delay decay rate dependence is obtained by using integral inequality,free-weight matrix method and zero-value equation technique.Thirdly,a model-dependent state feedback controller is deigned.The closed-loop systems are established,and the model-dependence and delay-dependence sufficient conditions are obtained by parameter setting and inequality tre.atment technique.The corresponding state,feedback control parameters are further derived.Finally,the effectiveness of the proposed method is verified by numerical examples and simulations.