Almost output regulation for switched linear systems with bumpless transfer control under destabilizing behaviors

Abstract

Almost output regulation for switched linear systems with destabilizing behaviors, which means that the almost output regulation problems of all subsystems are unsolvable and some switching instants are unstable with finite increments of the Lyapunov function, is investigated based on the bumpless transfer control. Switching instants with decrements and increments of the Lyapunov function are described as stable and unstable switching instants respectively. Firstly, a hybrid average dwell time strategy is proposed to restrict the occurrence ratio of unstable/stable switching instants and reasonably arranges the number of stable switching instants to offset the increment of the Lyapunov function caused by unstable switching instants and insolvabilities of the involved problem for all subsystems. Then, by interpolating the gains of adjacent controllers within the minimum dwell time, a dynamic error feedback controller with bumpless transfer property is designed to suppress the control bumps induced by controller switchings. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.