Abstract
This paper defines a condition of well-posendness for general linear systems and investigates its meaning. Originally, the condition was prorposed for basic linear systems such that a linear feedback is applicable to them. This paper claims that the condition is as basic a condition as causality and stationarity.
Let S⊂X×Y be a linear system and ρ20: X→Y its input response. Let L={K|K: Y→X} be the class of static linear feedbacks of S. Then (∀K∈L)((I-Kρ20): D(S)≅D(SK)) is called the well-posedness condition where SK is generated from S by a linear feedback K.
This paper shows that if the well-posedness condition is satisfied, (i) a state space representation of SK is explicitly determined by that of S, and (ii) the input response and the state response of a state space representation satisfy special properties.
One of the purposes of this study is to classify the equivalence of controllability and the mode controllability in the system theoretic sense. The results of this paper strongly suggests that the equivalence may be explained by the combination of causality, stationarity, finite dimensionality of the system core and the well-posedness condition.
