Research On Correlation Control Method Of Dynamic System With Time Delay

Time delay is common in real dynamical systems,which leads to poor performance and oscillation.The problem of stability analysis and controller synthesis for delayed dynamical system is an important topic in automatic control.Nowadays,we has lived in all kinds of delayed dynamical system in the world.Due to its widely applications in industrial process control,aerospace craft,medical,electric power and economy,de-layed dynamical systems has been taken into account by scholars and abroad.In this thesis,based on Lyapunov-Krasovskii functional(LKF)theory,the method of matrix de-composition,the techniques of inequality,control method(H_? control,robust control,intermittent feedback control)of several kinds of delayed dynamical systems is investi-gated.Some novel criteria are given to guarantee that the delayed dynamical system is finite-time stable,stochastically stable,finite-time synchronized,linear generalized outer synchronized.Several numerical examples are presented to demonstrate the effective-ness and advantages of the theoretical results.The main research work of this thesis is as follows:1.The problem of the finite-time H_? control for a class of continuous-time non-linear system with time-varying norm-bounded parameter uncertainties and admissible external disturbances is investigated.The state feedback controller and output feedback controller are designed which ensure finite-time boundedness and with a desired H_? performance index.Specifically,first,we structure some new LKFs,divide the time-varying delay into non-uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms exactly.Some sufficient conditions for existence of the robust state-feedback controller and output-feedback controller have been provided in terms of LMIs.2.The problem of output feedback control for a class of neural network with semi-markov parameters and time-varying is investigated.Due to the relaxed conditions on the stochastic process,the S-MJLSs are with time-varying transition rates and can de-scribe a broader class of dynamical systems than the traditional Markovian jump linear systems.Specially,first,by using an integral inequality based on a free matrix,the H_? performance analysis and mode-dependent nonrational synthesis conditions for the un-derlying S-MJLSs are developed,respectively.The free weight matrix technology is em-ployed to reduces the conservativeness of stability condition.By introducing the lower and upper of the transition rates(TRs)together with the sojourn-time fractionizing idea,the parametrized representation of the controller gains can be obtained in terms of the feasible solutions to a set of finite LMIs.3.The problem of robust mode-dependent control for a class of discrete-time sin-gular Markovian jump systems with time-varying delay is investigated.By using the Lyapunov functional method and delay decomposition approach,LMI-based sufficient conditions for the stochastic stability and robust mode-dependent control are developed,which guarantee the considered systems to be regular,causal and stochastically stabiliz-able.Wirtinger-based inequality and reciprocally convex approach are combined together to deal with the time-delay in the Markovian jump systems,new delay-dependent con-ditions with less conservatism are obtained.By using the stochastic analysis theory and introducing some inequalities,the problem to be solved can be converted into a convex optimization problem without applying the cone complementarity linearization proce-dure.For the first time the technique of time delay segmentation is applied to discrete time delay systems with markov parameters and this could reduce the conservatism of the results.4.The problem of robust control for a class of singular discrete time neural networks with partially unknown markov parameters is investigated.LMI-based sufficient condi-tions for the stochastic stability and robust control are developed.Then,a static output feedback controller and a robust static output feedback controller are designed to make sure the closed-loop systems are piecewise regular,causal and stochastically stable.5.The problem of cluster generalized outer synchronization in community networks via pinning control with two different switch periods is investigated.Several pinning controllers have been designed to achieve linear generalized outer synchronization.Using Lyapunov stability theory,sufficient linear generalized outer synchronization criteria for community networks are derived.6.The problem of finite-time synchronization for multi-link complex networks via intermittent feedback control is investigated.Firstly,by establishing a new differential inequality,constructing LKF and basing on finite-time stability theory,some novel cri-teria are given to guarantee that the error systems of drive-response systems are finite-time stable under intermittent feedback controllers.Secondly,some sufficient conditions ensuring the finite-time synchronization for a class of multi-link complex networks are obtained.The time delay between different layers is also taken into consideration.