Stabilization of deterministic and stochastic-parameter discrete systems

Abstract

A class of suboptimal control laws having the stabilizing property is used for treating linear discrete-time systems with deterministic and stochastic parameters. Known stabilization results, in the deterministic case, are extended to systems with singular state transition matrices and optimization horizon lengths shorter than the controllability indices of these systems. It is shown that in the case where the state transition and input matrices contain stochastic components, the stabilization of these systems in the sense of both almost-sure asymptotic and mean-square exponential stability is possible using the same line of reasoning.