Graphs, causality and stabilizability: linear, shift-invariant systems
on L-2 [0,infinity)
T.T. Georgiou and M.C. Smith
Abstract
This paper presents a number of basic elements for a system theory of
linear, shift-invariant systems on L-2 [0,infinity). The framework is
developed from first principles and considers a linear system to be a
linear (possibly unbounded) operator on L-2 [0,infinity). The
properties of causality and stabilizability are studied in detail and
necessary and sufficient conditions for each are obtained. The idea of
causal extendibility is discussed and related to operators defined on
extended spaces. Conditions for w-stabilizability and w-stability are
presented. The graph of the system (operator) will play a unifying
role in the definitions and results. We will discuss the natural
partial order on graphs (viewed as subspaces) and it