Stability Analysis And Robust Control Of Uncertain Linear Discrete Time-Delay Stochastic Systems

Stochastic phenomena widespread in various natural systems,which will more or less affect the system stability.In recent years,all kinds of studies about stochastic systems have become a research hotspot in control theory field.In addition,the theory of discrete control systems has got rapid development.In spite of online analysis,as well as outline analysis and computer,a discretization treatment is necessary to some extent.It is more necessary to strengthen the research on discrete-time stochastic system because that the discrete stochastic system represents an important mathematical model.Besides,actual system is easier to be affected by some uncertain factors and delay phenomenon caused by itself or outside world,which will result in the decrease of system performance and instability in sometimes.As a result,the research on discrete-time stochastic systems with uncertain and time delay parameters has important theoretical and practical value.Using Lyapunov function,Lyapunov-Krasovskii functional,stochastic operator spectrum and some other methods,this dissertation researched stability and robust control of several discrete stochastic systems based on linear matrix inequality and H representation tools,which includes discrete time-invariant stochastic systems with uncertainties and time delay,discrete time-varying stochastic systems with time delay and so on.And some related results of these several kinds systems have been obtained.The main work of this dissertation has the following aspects:1.We have researched quadratic stabilizability and H_? feedback control for stochastic discrete-time uncertain systems with state-and control-dependent noise.Specifically,the uncertain parameters considered are included both in system states and control and they are norm-bounded.Firstly,both quadratic stability and quadratic stabilization criteria arepresented in the form of linear matrix inequalities(LMIs).Then we design the robust H_?state and output feedback H_? controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_? controllable.Sufficient conditions for the existence of the desired robust H_? controllers are obtained via LMIs.Finally,some examples are supplied to illustrate the effectiveness of our results.2.We have researched the robust quadratic stability and stabilization of linear discrete-time stochastic systems with state delay and uncertain parameters.Firstly,the definitions about robust quadratic stable and stabilization have been given based on Lyapunov-Krasovskii functional.Then,a sufficient condition is,respectively,obtained for the stability and stabilizability of the considered system.Moreover,we design the robust H_? state feedback controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_? controllable.A sufficient condition for the existence of the desired robust H_? controller is obtained by means of the linear matrix inequality(LMI)method.Finally,an example with simulations is given.3.We studied the stability and stabilization of discrete-time stochastic time delay systems with general time-varying and slowly time-varying coefficients,respectively.Firstly,we make connections between the system under study and deterministic time-varying system.Then we investigate the exponential stability of the stochastic systems with regular time-varying coefficients by the spectral approach.So a generalization of spectral radius concept of a single operator is given.If the system parameters are slow,by assuming appropriate conditions,we gave the stabilization criteria of the corresponding slowly time-varying system.Finally,the concluding remarks are summarized and some future works which may be further investigated are pointed out.