Stabilization Of Two Classes Hybrid Stochastic Systems By Discrete-time Feedback Controls

In economic,biological and dynamical systems,hybrid Stochastic differential equations are widely used to characterize some systems affected by parameters and structural changes.Such systems are called hybrid stochastic systems.The stability analysis of hybrid stochastic systems is the analysis of the long-term behavior of the systems solutions.For an unstable stochastic system,feedback controls can be designed in the drift part based on the continuous observations of the system states and modes to make the controlled system stable.However,it is difficult and costly to observe the states and modes of the system continuously when the controller is designed in practice.Therefore,feedback controls based on discrete-time observations is considered in this paper to reduce the observation cost to some extent.The moment exponential stability of the order p>2 for discrete-time-observed controlled hybrid systems has been discussed by many scholars.But the generalized moment exponential stability(p>0)of such systems is not complete.So on the one hand,we discuss the more generalized moment exponential stability criterion(p>0)for the controlled hybrid stochastic systems in this thesis.The results of Hu in [34] are applied to the study of discrete-time feedback controls.On the other hand,the solutions of some hybrid systems depend not only on the current states but also on the past states.The asymptotic stability of equilibrium points for hybrid stochastic systems with time-delay,such as probability stability,almost sure exponential stability and moment exponential stability,has been discussed comprehensively.But in some practical problems,the asymptotic stability of the equilibrium point of the solution is too strong.Meanwhile,sometimes it is not necessary to be so strong.In this case,it is meaningful to study a more general class of stability: whether the solution converges in terms of its distribution(without converging to zero).This property is called asymptotical stability in distribution.Moreover,proving of stability in distribution of hybrid systems is significant different from that of classical stability.Therefore,stabilization in distribution of hybrid delay systems is also studied in this paper.This thesis is divided into two parts:1.Firstly,stochastic systems with Markovian switching are considered.Under the global Lipschitz condition,it is proved that an unstable hybrid stochastic system can be stabilized by discrete-time feedback controls in the sense of exponentially stability of pth moment(p>0).This goal is achieved by comparing to the continuous-time feedback-controlled hybrid systems.The upper bound for the duration between two consecutive observations is also obtained.Finally,a numerical example is stated to support the theoretical results.2.In the second part,this paper studied stabilization in distribution of hybrid stochastic delay systems by discrete-time feedback controls.A proper Lyapunov functional is employed for the research goal under the global Lipschitz condition.The uniform boundedness and exponential searching property of controlled hybrid systems are discussed.The sufficient conditions for stability in distribution are given.The control design is established and the upper bound for the duration between two consecutive observations is obtained.Finally,a numerical example is illustrated to support the theoretical results.