Class Of Time-varying Stochastic Systems Research Articles

Exact detectability and exact observability of discrete-time linear stochastic systems with periodic coefficients

This paper is devoted to the problem of detectability and observability of a class of time-varying stochastic systems. The main contribution of this note is to propose a PBH-type test which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some non-zero output. Then, we apply the obtained results in order to derive a criterion of exponential stability in mean square sense as well as existence conditions for the stabilizing solution of a class of discrete-time time-varying Riccati equations.

Limiting optimal discounted-cost control of a class of time-varying stochastic systems

We consider a class of time-varying R d -valued control models, and with possibly unbounded costs. The processes evolve according to the system equation x n+1 = G n ( x n , a n )+ ξ n ( n∈ N ), where { ξ n } are i.i.d. random vectors and { G n } a sequence of known functions converging to some function G ∞. Under suitable hypotheses, we show the existence of an α-discount optimal policy for the limiting system x n+1 = G ∞( x n , a n )+ ξ n .

Identification of stochastic time-varying systems

The parameter identification of a class of time-varying stochastic systems is considered in this paper. Online schemes which track the time-varying parameters in real time are proposed. Conditions which guarantee either almost sure convergence of the estimation error to the null or bounded mean-square error are obtained. The analysis is based on stochastic Lyapunov functions. This allows the convergence conditions to be weakened, and makes investigation of the stability problem of the proposed identification schemes possible.