Exact Observability Of Stochastic Time-Varing Systems And Weak Stability Of Discrere-Time Stochastic Time-Invariant Systems

This thesis investigates the exact observability of stochastic time-varying linear systems and weak stability of discrete-time stochastic time-invariant systems, and their applications to the problems of control via lto formula and linear matrix inequality approach.Firstly, the exact observability of stochastic time-varying linear systems is studied. With the aid of Ito formula, a matrix "H" is found, then the relationship between the coefficient matrix of linear time-varying systems and stochastic time-varying linear systems is given. Next, "Gramian Matrix Criterion" is obtained to test the exact observability for both continuous-time linear stochastic time-varying systems and discrete-time linear stochastic time-varying systems, respectively. Moreover, the "Rank Criterion" can also be given by this equivalence relationship. Compared with Gramian matrix criterion, rank criterion is more useful in practice. Then through discussing the exact observability of stochastic time-varying linear systems, some significant conclusions are presented.Secondly, the weak stability of discrete-time stochastic time-invariant systems is studied. Above all, the concept of stabilizability of feedback closed-loop system is given by using a feedback control, and the concept of the weak stability of discrete-time linear stochastic time-invariant system is introduced, then we find an arithmetic progression. Thus by using the relationship between the initial state and the state of anytime, a necessary and sufficient condition is given for the weak stability of discrete-time stochastic time-invariant systems.