IMPULSIVE-SMOOTH BEHAVIOR IN MULTIMODE SYSTEMS .1. STATE-SPACE AND POLYNOMIAL REPRESENTATIONS

A 'switched' or 'multimode' system is one that can switch between vari ous modes of operation. We consider here switched systems in which the modes of operation are characterized as linear finite-dimensional sys tems, not necessarily all of the same McMillan degree. When a switch o ccurs from one of the modes to another of lower McMillan degree, the s tate spare collapses and an impulse may result, followed by a smooth e volution under the new regime. This paper is concerned with the descri ption of such impulsive-smooth behavior on a typical interval. We prop ose an algebraic framework, modeled on the class of impulsive-smooth d istributions as defined by Hautus. Both state-space and polynomial rep resentations are considered, and we discuss transformations between th e two forms. Copyright (C) 1996 Elsevier Science Ltd.