On model matching problems of input-output switching systems

In this paper we consider the model matching problem where linear switched systems are involved. We focus on the worst-case l_∞ induced norm and consider the problem when the involved systems have independent or matched switching sequences. We show that a switched compensation which can switch independently of the plant has no advantage over an LTI compensation. Moreover, if the plant is strictly causal, even a switched compensation which has the same switching as the plant does not provide a better performance over an LTI compensation. We further generalize the results of [1] to MIMO systems and present an exact expression to compute the worst-case l_∞ induced norm. Using that, one can cast a class of model matching problems as a Linear Programming.