IMPULSIVE-SMOOTH BEHAVIOR IN MULTIMODE SYSTEMS .2. MINIMALITY AND EQUIVALENCE

This is the second part of a two-part study of linear multimode system s. In the first part, it was argued that the behavior of such a system on an interval between switches should be described in a framework th at allows for impulses at the switching instant, and both first-order and polynomial representations were introduced that satisfy this requi rement. Here we determine the conditions under which first-order repre sentations are minimal. We also show how two minimal representations o f the same behavior are related; this leads in particular to an approp riate state-space isomorphism theorem. The minimality conditions are g iven a dynamic interpretation. Copyright (C) 1996 Elsevier Science Ltd .