Necessary and Sufficient Conditions for Analysis of L2 Gain across Switching

Switching in control systems often causes bumpy responses. Recently, some methods have been proposed to analyze L2 gain from disturbance inputs before switching to control outputs after switching for systems with uncertainty. However, the results are conservative, since the analysis is aimed for robust performance problems and the conditions given in those methods are sufficient conditions. On the other hand, by considering the corresponding nominal case, this paper gives necessary and sufficient conditions. The resultant conditions are given in terms of both Lyapunov equations and linear matrix inequalities. Moreover, the results provide generalization of the Hankel norm analysis. A numerical example shows the effectiveness of the proposed gain and the analysis conditions.