The Study Of Stability Analysis And Synthesis For Several Classes Of Stochastic Nonlinear Systems With Time Delay

The nondeterministic (i.e. stochastic) phenomena are frequently encountered in practice industrial control. These systems’dynamic characteristics are generally difficult to use precise mathematical model to describe, and often show random characteristics. Moreover, the problem of nonlinearities is an important research object faced by the field of nature, engineering technology and the economics. So the difficulties of the investigation for control systems are stochastic and nonlinear, which is more practical in application. It is because of this reason that many basic and typical problems of control theory are unfathomed for a long time. Thus, the investigation for the control theories of stochastic nonlinear systems is a challenge and worthy to investigate, which is more practical in application. As concerned above, in this dissertation, by employing linear matrix inequality (LMI) technique and stochastic control theory, the sufficient conditions are obtained such that the resulting systems are robustly asymptotical or exponential stable in the mean square, for all possible nonlinear disturbances, external stochastic disturbances, Markovian jumping, time delays as well as uncertain parameters. Some novel methods and ideas in the fields of stochastic nonlinear systems with time delay are proposed. The main contents of the dissertation can be briefly described as follows:1. The problem of dynamics analysis for a class of new impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays is researched. Some criteria for the asymptotical stability in mean square are obtained based on LMI forms and stochastic control theory. Com-pared with the existing results, this paper considers not only discrete time-varying delay but also distribute time-varying delay. And the derived criteria can be verified easily checked and solved by LMI Toolbox in Matlab. The proposed methods are extended to the stochastic impulsive Cohen-Grossberg neural networks with either norm-bounded uncertainties or time delay.2. The robust stability problem of a class of uncertain neutral stochastic neu-ral networks with Markovian jumping and time-varying delays is researched. First, a new model of uncertain neutral stochastic neural networks with stochastic disturbance and Markovian jumping. The parameter uncertain-ties are assumed to be time-varying and norm-bounded. Based on Lipschitz continuity and Schur complement method, the delay-dependent sufficient con-ditions for the above problem are obtained, which is less conservative than the delay-independent ones.3. The fuzzy control problem of a class of new stochastic distributed parameter system with time delay is researched. First, a new model of distributed param-eter system with multidimensional Brownian motion and time-varying delay. Based on Galerkin’s method and fuzzy control theory, the delay-dependent cri-terion of the closed-loop system for the asymptotical stability in mean square are obtained. Finally, the guaranteed cost control problem of the above system is researched, and given the method of fuzzy controller and guaranteed cost controller by using of the solution of linear matrix inequality.4. The global asymptotical stability problem of stochastic fuzzy Hopfield neural networks with time-varying delays is investigated. Based on the Lyapunov-Krasovskii functional approach, an improved free-weighting matrix approach with weighting-dependent Lagrange multipliers, and the Jensen integral in-equality, novel LMI-based stability criteria are developed by applying a parameter-dependent Lyapunov functional and new fuzzy relaxed techniques for cubic fuzzy summations. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability anal-ysis and the obtained relaxed stability criteria are in terms of Linear matrix inequalities.5. The stochastic stability problem of neutral-type impulsive neural networks with Markovian jumping and mixed time-varying delays described by a integro-differential equations is concerned. This structure under consideration is more general that those in the other papers. By utilizing the Lyapunov-Krasovkii functional approach, we obtain some novel global exponentially stable results, which are delay-dependent sufficient condition. The proposed methods are extended to the stochastic impulsive neutral neural networks with time-varying delay, which is different from each other.6. The problem of delay-dependent stochastic stability analysis for nonlinear Markovian jumping neural networks with mixed time-varying delays and multi-plicative noise is considered. By introducing slack matrix variables and Marko- vian jumping Lyapunov functional, some new delay-dependent sufficient con-ditions are obtained in linear matrix inequality (LMI) format which guarantee the system is asymptotically mean-square stable. An important feature of the model is that mixed state delays and multiplicative noise are mode-dependent.Finally, concluding remarks are given. Some unsolved problems and devel-opment directions for stochastic neural networks with time delay and stochastic distributed parameter system are illustrated. Further, the prospects of the future study are given.