Dynamic regulators in discrete systems with controllable and observable outputs

Abstract

Necessary and sufficient conditions for the static output feedback stabilizability of linear discrete-time systems is derived. The conditions take the form of a matrix inequality. It is shown that an algorithm of stabilization, which follows from these condition, is applicable for a certain class of nonlinear discrete-time control systems. An algorithm for constructing the control laws providing a given estimate of the weighted damping level of input signals and initial perturbations and robust stability of the equilibrium state of the control system is proposed. The results are illustrate$d by an numerical example for a discrete-time stabilization system.