Worst-Case L₂ Gain Analysis of Systems with Controller Switching and Dynamic Uncertainty

Abstract

This paper deals with analysis of worst-case L₂ gain in terms of bumpy responses due to disturbance for systems with controller switching. Control systems often have bumpy responses caused by switching controllers. Those responses are harmful, since they not only degrade control performance but also may damage plants, actuators and so on. Several methods have been proposed to attenuate bumpy responses. However, most of those methods lack performance and/or robustness guarantee against disturbance and/or uncertainty. In particular, no exact definitions of bumpy responses have been formulated. This paper first defines bumpy responses to be dealt with. Based on the definition, we propose a method to analyze the responses by using LMIs. The method can be applied to the worst-case Hankel norm analysis. The effectiveness of the proposed method is examined by using a numerical example.