Robust guaranteed cost control of linear systems with norm bounded uncertainties and external disturbance

This paper proposes a robust guaranteed cost control method for a linear system with norm bounded time varying parametric uncertainties and external disturbance. Using the Lyapunov stability theory and linear matrix inequality method, a robust guaranteed cost control law is derived to guarantee that the closed loop system is not only stable, but also has adequately quadratic and H_∞ performance levels for all the admissible uncertainties and external disturbance. A convex optimization problem is formulated to obtain the optimal state feedback controller which can minimize the quadratic and H_∞ performance levels. Based on the model of the robot prototype for inspecting power transmission lines, simulation results verify the effectiveness of the proposed method.