Synthesis of decentralized robust stabilizing control for the systems with parametric perturbations

System Analysis and Control

The paper considers the problem of robust stabilization of large-scale systems with parametric perturbations within set number intervals. Design of systems with robust properties is among the most important problems of control theory. It allows to describe dynamics of the initial object by a mathematical model using a vector differential equation with interval coefficients. The paper states the problem of synthesis of stabilizing control with a pre-assigned degree of robust stability for closed systems. Scalar optimization function and Lyapunov–Razumikhin function were used to identify many stabilizing regulators. Parameters of robust control regulators are determined by the solutions of two Riccati equations: the first one corresponding to the nominal parameters of the object and the second – to variations of the object parameters. Sufficient conditions for robust stability of the closed system are obtained.