RESEARCH OF STABILIZATION CONDITIONS AND ROBUST STABILITY OF DISCRETE ALMOST CONSERVATIVE SYSTEMS

Abstract

Conditions for the stabilizability of discrete almost conservative systems in which the coefficient matrix of a conservative part has no multiple eigenvalues are investigated.It is known that a controllable system will be stabilized if its coefficient matrix is asymptotically stable.The system stabilization algorithm is constructed on the basis of the solvability condition for the Lyapunov equation and the positive definiteness of P0 and Q1.This theorem shows how to find the parameters of a controlled system under which it will be asymptotically stable for sufficiently small values of the parameter e (P > 0, Q > 0).In addition, for a small parameter e that determines the almost conservatism of the system, an interval is found in which the conditions for its stabilizability are satisfied (Theorem 2).