Stability Analysis Of Stochastic Systems With Time-delay

Stochastic stability theory is used to study system’s stability when there are randomdisturbances. Due to the feasibility in method and rationality in engineering, it has recrivedextensive attention since its coming into being. At present, stochastic stability theory is still ahot research problem for experts and scholars.As we all know, time-delay is often an important source of instability or performancedegradation in a practical system. So its existence presents difficulties for stability analysisand control theory. In recent years, the reacherch of systems with time-delay is very active,and has penetrated into many fields, such as stability analysis of systems with time-delay,guaranteed cost control, H control,etc. Since they have less conservative than delayindependent’s stability conditions, delay-dependent’s stability conditions of systems withtime-delay have been greatly concerned. Moreover, stochastic systems with time-delay candescribe real systems more accurately than others. So the study of stability and control forstochastic systems with time-delay has a great value both in theory and application.In this paper, based on the Lyapunov stability theory, using free-weighting matrix approachand the linear matrix inequality method, the problem of stability analysis and H control forstochastic systems with time-delay is investigated. The main content of this thesis are statedas follow:1.The problem of stability for uncertain stochastic system with time-delay is considered.Based on designing a Lyapunov-Krasovskii functional, using free-weighting matrix approach,a stability criterion is derived to ensure that the nominal system is stable and the sufficientcondition is expressed with LMIs. Then the condition is popularized to uncertain systems byusing a related lemma.2. The problem of control for stochastic systems with time-delay is considered. Based onLaypunov function, a controller is designed which can make the closed loop systemasymptotical stability and have given H performance. The existing conditions of controllercan be expressed with LMIs. Further, the method of designing can be determined by using theLMI toolbox in Matlab.3.The problem of stability for neutral stochastic system with time-delay is considered. Adelay-dependent stability criterion is derived when neutral delay is the same with discrete _delay. And a delay independent stability criterion is derived when neutral delay is differentfrom discrete delay. Moreover, the upper bound of discrete delay will increase with thedecrease of neutral delay.4.The problem of mean square exponential stability for stochastic system with time-delay isconsidered. Since free-weighting matrix approach is computation-intensive andtime-consuming, I have improved the process of proof by using Martingale theory.