Synthesis of multiple model switching controllers using [formula omitted] theory for systems with large uncertainties

Abstract

The switching based control is an effective way to handle systems with large and fast varying uncertainties. Many conventional methods, however, do not use robust controllers to stabilize each model, and thus need a large number of controllers to ensure the stability of systems with large uncertainties. Under the structure of supervisory control, this paper presents a robust multiple model switching control (RMMSC) method using H∞ control for MIMO linear systems with large parametric uncertainty. The proposed method uses H∞ controller to maximize the stability region of each model with uncertainties, and thus to significantly reduce the number of candidate controllers. The candidate controllers are designed by using linear matrix inequality (LMI), and an exponentially decaying switch index is proposed to select the proper controller by estimating the system norm of each model uncertainty. Using such switch index, the closed-loop control system is then equivalent to a switching system with smaller uncertainty whose system norm can be predefined by designers. The robust stability under arbitrary switching conditions is proven by the small gain theorem; and for slow switching conditions, the acceptable dwell time for stability is analyzed and presented. The effectiveness of this method is demonstrated with the second order inertial system with large model uncertainties.