Research On Stability Analysis And Control Of Stochastic Fuzzy Systems With Aperiodic Sampled-data

Stochastic factors occur everywhere in both the real world and the external environ-ments of social and engineering systems,and have effect on the dynamical behavior of the systems.As a result,the It(?) stochastic systems which take the stochastic factors as the inner driving factor of themselves are always adopted to reflect the evolution laws of the natural and the social engineering.Meanwhile,with the development of technology,the real plants usually face the fact that their structure or the parameters are very complex,time varying,nonlinear,strong coupling and time-delayed and so on.With the property that the T-S fuzzy models are able to approximate the nonlinear systems with arbitrar-ily accuracy,and we can make use of the related theories on linear systems to analysis the nonlinear problems,the T-S fuzzy systems are attracted numerous attentions and have widely application after they have been proposed.Besides,as the computers are deeply improved,researches and industrial processes are always used them as the digital controllers in recently years with the advantages such as high accuracy,stability ect.En-lightened by these ideas,in this dissertation,we take the stochastic nonlinear systems as the analysis plants,for which the method of T-S fuzzy systems can be adopted and the controllers are implemented with sampled-data.In the dissertation we mainly explore the stability and several control problems of the stochastic fuzzy systems with aperiodic sampling.The main contents and innovative points of this dissertation are presented as follows:1.The background and significance of stochastic fuzzy systems and sampling control are introduced.The current situation for the research on It(?) stochastic systems,time delay systems,the T-S fuzzy systems and control,sampling control and fuzzy control with sampled-data are reviewed respectively.Then some preliminaries,related theorems,lemmas and definitions are presented.At last,the main research contents and chapters arrangement are introduced.2.From a new respective,we investigate the mean-square stability of the stochastic fuzzy systems with aperiodic sampled controller.The means to cope with the sampled-data in this chapter is the input-delay method.Then the continuous systems with discrete feedback problem is transformed to be the feedback problem with input time-varying de-lay.The analysis tool is chosen as the Lyapunov function method.By make use of the equation repeatedly,take advantages of the delayed feedback,the time delay is not only damaged to the stability of the systems,but also contributes to the systems.Besides,we try to make connection between the delayed state and non-delayed state,then the latter is used to estimate the former,finally we get a more relax theorem which represented as Riccati matrix equations and not utilize the Razumikhin technique.With this kind of the theorems,we are able to see the contributions the controllers clearer.3.The robust guaranteed cost control problem of stochastic fuzzy systems with ape-riodic sampling is considered.In order to vividly represent the sawtooth structure of the aperiodic sampled-data and to depict the continuous systems with discrete signals more precisely,in this chapter,we use the hybrid modeling method to cope with the aperiodic sampled-data,i.e.a kind of the stochastic impulsive control problem.The remodeled system is able to avoid the unmatched problem of the fuzzy systems and the fuzzy con-trollers.Furthermore,we use the time-varying Lyapunov method to analysis the stability and controller synthesize problem while the spectral radius of the gain matrix remodeled impulsive control system is not less than 1.4.The robust H_?control problem of uncertainty delayed stochastic fuzzy systems with aperiodic sampled-data is investigated.The hybrid modeling method is used to cope with the sampled-data,and feedback manner is chose to be the multirate feedback.In order to match the aperiodic sampling cases,we design the quasi-periodic multirate state feedback controller,and the usual single-rate controller is the special case of the multi-rate one.The analysis tool is time-varying Lyapunov function method.Influenced by the delayed factors,the time-varying matrix function is delayed accordingly.Therefore we design a new algorithm to determine the exact value of the delayed matrix function.Finally,we get the sufficient condition of the uncertainty stochastic fuzzy systems satis-fied the H_?performance.5.The H_?filtering problem of stochastic fuzzy systems is considered with aperiodic sampled-data.We use the hybrid system modeling technique to deal with the aperiodic sampled-data,in this chapter,the final model is the impulsive model.Then we design a full-order fuzzy filtering for the stochastic fuzzy system.Use the time-varying Lyapunov function method,we analysis the mean-squared exponential stable and H_?performance of the filtering error system,and then we designed the parameters of the filter.Since the design of filter is a kind of dynamic algorithm,we proposed a new direction to the research of dynamic feedback based on hybrid system.Finally,the conclusions and some topics for future work are given.