State Space Representation of a General Time System
Yasuhiko Takahara · Transactions of the Society of Instrument and Control Engineers · 1973
In this paper we discuss when a time system can be represented by a canonical form.The concept of a time system has been introduced as a general abstract model of dynamic systems. Since the model is defined as an input-output (set theoretic) relation, it is so general that it can cover almost all dynamic systems. On the other hand, in modern systems theory most of the arguments and results of dynamic systems are based on their state representation. Hence, it is an interesting problem in general systems theory to find how a general time system can be represented by a state space.This paper takes the automaton type state representation as a canonical form for dynamic systems and discusses how a state space and the canonical representation can be introduced for a general time system and, hopefully, places a theoretical foundation to the state space approach.