Stabilization of some stochastic discrete–time control systems

Abstract

In the first part of the paper linear–quadratic control problem under indenendent random perturbations is considered. Under a controllability assumption it is shown that every linear admissible feedback control stabilizes the control system. Using this fact,a procedure to construct a monotone decreasing sequence of quadratic forms which converges to the optimal value of the control problem is discussed. Similar results for the linear–quadratic control problem under jump Markov perturbations are also obtained. In the last part of the paper, some necessary conditions for the stabilizability of a class of linear discrete–time control systems with independent random perturbations are derived