Robust time-weighted guaranteed cost control of uncertain periodic piecewise linear systems

Abstract

This paper studies the design problem of periodic piecewise guaranteed cost controllers for a class of continuous-time uncertain periodic piecewise linear systems using a time-weighted quadratic cost function. By developing Lyapunov functions with quadratic cost matrices to a time-varying form, sufficient conditions are proposed to ensure the exponential stability of the closed-loop system and a guaranteed upper bound of the cost function. To minimize the upper bound in the controller design process, an iterative algorithm is developed to solve the problem via convex optimization. The effectiveness of our proposed algorithm is demonstrated via a numerical example, and the impact of time-weighted cost is illustrated by simulation results.