### Almost sure tracking for linear discrete-time periodic systems with independent random perturbations.

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In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.

In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see [], for finite dimensional stochastic equations or [], for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see [], []). Under stabilizability...

A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, the techniques for obtaining its properties are not, and we make use of the theory of abstract Banach algebras and weighted spaces. It is hoped...

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