The Stationary State/Signal Systems Story

Abstract

We give an introduction to the theory of linear stationary s/s (state/signal) systems in continuous time. A s/s system has a state space which plays the same role as the state space of an ordinary i/s/o (input/state/ output) system, but it differs from an i/s/o systems in the sense that the interaction signal which connects the system to the outside world has not been divided a priori into one part which is called the “input” and another part which is called the “output”. The class of s/s systems can be used to model, e.g., linear time-invariant circuits which may contain both lumped and distributed components. To each s/s system corresponds in general an infinite number of i/s/o systems which differ from each other by the choice of how the interaction signal has been divided into an input part and output part. Each such i/s/o system is called an i/s/o representation of the given s/s system.

We begin by giving an introduction to the time domain theory for i/s/o and s/s systems, then continue by taking a brief look at the frequency domain theory for i/s/o and s/s systems, and end with a short overview of the notions of passivity and conservativity of i/s/o and s/s systems. In all cases the s/s results that we present can be formulated in such a way that they do not depend on any particular i/s/o representation of the s/s system, but it is still true that there is a strong connection between the central properties of a s/s system and the corresponding properties of its i/s/o representations.