Smooth/impulsive linear systems: interconnections

Abstract

Smooth/impulsive (sm/imp) linear systems are the smallest class containing all classical linear systems and stable with respect to limits. In this article we show that they behave well under the operation of interconnection. Namely, it turns out that the McMillan degree of a regular interconnection is always equal to the sum of the McMillan degrees of the components. In other words, all regular interconnections of sm/imp linear systems automatically are regular feedback interconnections. For this more general class of linear systems, we also study the regular interconnection problem.

Keywords:

• sm/imp linear system
• AR-model
• Mikusinski function
• interconnection