Study On Stability And State-Feedback Control For Stochastic Systems

Stochastic neural networks have been playing a key role in artificial intelligence,image processing,optimal control,fault diagnosis,signal processing and other fields.Especially the stability and control of stochastic neural networks with delays are hot research topics.Moreover,the state-feedback control of stochastic nonlinear systems has attracted extensive attention.It is of great academic value and practical signifi-cance to study the input-to-state stability and practical stability of stochastic nonlinear systems under event-triggered and self-triggered state-feedback control.In this thesis,the stability of two classes of stochastic neural networks with expectations in coef-ficients and three classes of stochastic nonlinear systems with state-feedback control are mainly considered.The details are as follows:First,the stability of the stochastic delayed neural network with expectation in coefficients1.A class of stochastic fuzzy Cohen-Grossberg neural networks with time-varying delays is studied.Different from previous literatures,expectation is added to the drift and diffusion coefficients of the model.The influence of average state on neural networks is considered.Using stochastic analysis theory,Lyapunov-Krasovskii functional and two different scaling techniques,the mean square exponential stability of the solution of the model under different conditions is obtained.Then a variable parameter is used to compare the applicable scope of above two methods.2.A class of stochastic neural networks with expectations,time-varying delays and leakage delays is studied.First,by using the stopping theorem,Fatou lemma,a new theorem that makes the model stable is given based on the Lyapunov function V(t,x).With the help of the above theorems,Ito's formula and matrix inequality technique,a stability theorem with more easily verifiable conditions is obtained.In addition,we degenerate the conclusion to a simple case without the leakage delay.Finally,we illustrate the validity of the theorem by an example.Second,the stability of different stochastic nonlinear systems under the state-feedback control1.A class of stochastic fuzzy Cohen-Grossberg neural networks with the state-feedback control and an unknown external disturbance is studied.Through the pro-posed event-triggered mechanism with longer triggering time interval,Lyapunov function,Dynkin formula,comparison principle and other methods,the input-to-state stability of the solution of the model is obtained.In addition,the theorem shows that any two triggering time will not converge to the same convergence point.Moreover,the lower bounds of the adjacent two triggering time intervals are estimated.Finally,an example is given to illustrate the influence of different values of the designed event-triggered mechanism parameters on the length of the triggering time interval and the number of triggering times.2.A class of stochastic nonlinear discrete-time systems under event-triggered control is studied.The effects of external disturbances on stability of the system under two cases of state-dependent and state-independent are discussed respectively.By means of the discrete event-triggered mechanism and K L-function properties,as well as consistent Lipschitz condition,proof by contradiction,classification discussion and other methods,the asymptotic stability in mean square of the discrete-time system is realized.In particular,in the case of the state-dependent disturbance,we assume that the disturbance can be controlled by a state-related function.Thus,the asymptotic stability in mean square of the system can be obtained.On the other hand,in the case of state-independent disturbance,we get the input-to-state stability in mean square of our suggested system.3.A class of stochastic nonlinear continuous-time systems with Markovian switching under the state-feedback control is studied.First,we give the p-moment practically exponential stability and the p-moment practically asymptotic stability based on the event-triggered mechanism for stochastic systems with an external disturbance.Since the elements of the event-triggered mechanism cannot be directly observed,we have developed a self-triggered control rule to overcome this difficulty.By applying the improved monotonic growth condition,Ito's formula,Fubini's theorem,Gronwall inequality and comparison principle,we establish a novel lemma to estimate the lower bound of second-order for state and the upper bound of second-order for error.Moreover,we also establish the practically asymptotic stability in mean square with the help of Jensen's inequality,the properties of K-function and the result on p-moment input-to-state stability.Furthermore,from Lipschitz continuity and monotonicity of functions,we obtain the value of the maximum triggering interval based on lasted-observed state.Finally,an example is used to calculate the maximum triggering time interval that can guarantee the stability of the suggested system.