A linear matrix inequality–based approach for estimating upper bound of settling time

Abstract

In this article, an upper bound on the settling time is provided for exponentially stable systems by the Lyapunov theory. In order to obtain a more accurate estimate on the upper bound of settling time, an optimization problem with a nonlinear objective function needs to be solved. Since this is a complex problem, a linear matrix inequality–based algorithm is proposed to solve it. Then, we address the stability analysis problem of linear systems with the aim to derive the upper bound on the settling time. This problem is extended to design a static feedback controller for linear systems under input saturation. By solving the optimization problem, the upper bound of the settling time for the closed-loop system is minimized. Finally, the validity and effectiveness of the proposed method are verified by the simulation results and comparisons.