An LMI approach to control of exponentially unstable systems subject to saturation and time-varying delay in the input

Abstract

This chapter studies the stabilization of exponentially unstable linear systems subject to saturation and time-varying delay in the input. The proposed stabilizing controller is developed in a two step process. First, the stabilizing controller for the system without saturation is obtained from the optimal solution to an iterative LMI problem, such that the upper bound of the delay function ismaximized. Second, the input saturation is included in the analysis, and the previous iterative LMI problem is updated in order to maximize the domain of attraction of the closed-loop system. The effectiveness of the proposed methods is demonstrated through numerical examples, and by experimental validation on a test rig that captures the main operating characteristics of active magnetic bearings.