Constrained control of discrete-time stochastic systems

Abstract: The purpose of the paper is to present a class of algorithms using to solve the optimization problem concerning with H∞ feedback control for linear discrete-time stochastic systems with stochastic parameter uncertainties, as well as a method for the optimization problem reducing this to a standard formulation used two convex inequalities, which can be solved by linear matrix inequality (LMI) methodology. Some generalized considerations for the algorithm procedures are given and the problem of LMI set-up, using the technique based on Schur complement, for calculating the terminal weight matrix P is outlined. Finally, obtained results are adapted by that way to design constrained H∞ feedback control for system which state variable satisfy equality constraints in the mean. The procedure results the constant feedback for the linear controller defined in terms of matrix inequalities and a matrix equality.