Properties of the Well-Posedness Condition for Linear Feedback Systems

Ikeshoji, Hideomi; Saitô, Toshio; Takahara, Yasuhiko

doi:10.9746/sicetr1965.18.37

Cited by 2 publications

(8 citation statements)

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“…DEFINITION I Basic linear system [Takahara, 1981] Let a time set T be R+ or TZ+ for some T E R+. A time system sex x Y over a field A is called a basic linear system if the following conditions are satisfied.…”

Section: Introductionmentioning

confidence: 99%

“…In mathematical general systems theory Takahara [1981] has characterized linear systems as basic linear systems. A basic linear system has a unique state space representation, and it makes behavioral consideration of linear system possible.…”

Section: Introductionmentioning

confidence: 99%

“…One of the most profound properties of a basic linear system is that it has a unique state space representation up to isomorphism [Takahara 1981]. Also a unique initial response function of a basic linear system sex x Y exists, which is called the …”

Section: Introductionmentioning

confidence: 99%

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mentioning

confidence: 99%

“…In this paper the concept of a basic linear system [Takahara 1981] is used to explore relations between continuous-time and discrete-time systems from two directions.…”

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confidence: 99%

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Relations Between Continuous-Time and Discrete-Time Linear Systems

Sato

1993

International Journal of General Systems

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In this paper the concept of a basic linear system [Takahara 1981] is used to explore relations between continuous-time and discrete-time systems from two directions.First, preservation of systems structure through sampling is considered. Two sampling methods are defined and it is shown that both preserve linearity, causality, stationarity. and finite dimensionality of system core. These preservation makes the resultant discrete-time system a basic linear system.Secondly. we investigate what is the minimal basic linear system for all of discrete-time basic linear systems which are made from sampling of a basic linear system. A continuous-time basic linear system is said to be minimal in the sense that any element of the set of discrete-time basic linear systems can be embedded into it and there is no greater basic linear system that can embed them. It is shown that the original continuous-time basic linear system is the minimal system.INDEX TERMS: Basic linear system, simple sampling, O-th hold-sampling; discrete-time system, continuous-time system, category of basic linear systems, minimal embedding of sampled systems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

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mentioning

confidence: 99%

“…In this paper the concept of a basic linear system [Takahara 1981] is used to explore relations between continuous-time and discrete-time systems from two directions.…”

mentioning

confidence: 99%

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