Stabilization and Attenuation of Bounded Perturbations in Discrete Control Systems

Abstract

Necessary and sufficient conditions for the static output feedback stabilization of linear discrete-time control systems are formulated in the form of a matrix inequality. It is shown that the algorithms of stabilization based on these conditions are applicable to a certain class of nonlinear discrete-time control systems. We propose the procedure of construction of the regularities of control guaranteeing the required estimation of the weighted level of attenuation of input signals and initial perturbations, as well as the robust stability of the equilibrium state of the controlled system. A numerical example of the discretetime system of stabilization of a pendulum on a moving platform is presented.