Impulsive-smooth behavior in multimode systems part I: State-space and polynomial representations

Abstract A ‘switched’ or ‘multimode’ system is one that can switch between various modes of operation. We consider here switched systems in which the modes of operation are characterized as linear finite-dimensional systems, not necessarily all of the same McMillan degree. When a switch occurs from one of the modes to another of lower McMillan degree, the state space collapses and an impulse may result, followed by a smooth evolution under the new regime. This paper is concerned with the description of such impulsive-smooth behavior on a typical interval. We propose an algebraic framework, modeled on the class of impulsive-smooth distributions as defined by Hautus. Both state-space and polynomial representations are considered, and we discuss transformations between the two forms.

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