Convolution algebra representation of systems described by linear hyperbolic partial differential equations

S. P. Levkov; Józef Korbicz

doi:10.1080/00207178908559760

Convolution algebra representation of systems described by linear hyperbolic partial differential equations

S. P. Levkov, Józef Korbicz

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Abstract

The representation of the input-output operator in convolution algebra B(σ₀) is obtained for distributed parameter systems described by linear hyperbolic partial differential equations. Three kinds of system are considered depending on the kind of coefficient matrix corresponding to the space variable derivative, and their properties are studied. Necessary and sufficient conditions for stability are obtained in terms of factorization of the transition matrix. The obtained results allow the use of modern algebraic methods for analysis of such systems.

Original language	English (US)
Pages (from-to)	2029-2044
Number of pages	16
Journal	International Journal of Control
Volume	49
Issue number	6
DOIs	https://doi.org/10.1080/00207178908559760
State	Published - Jun 1989
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications

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10.1080/00207178908559760

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abstract = "The representation of the input-output operator in convolution algebra B(σ0) is obtained for distributed parameter systems described by linear hyperbolic partial differential equations. Three kinds of system are considered depending on the kind of coefficient matrix corresponding to the space variable derivative, and their properties are studied. Necessary and sufficient conditions for stability are obtained in terms of factorization of the transition matrix. The obtained results allow the use of modern algebraic methods for analysis of such systems.",

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year = "1989",

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AB - The representation of the input-output operator in convolution algebra B(σ0) is obtained for distributed parameter systems described by linear hyperbolic partial differential equations. Three kinds of system are considered depending on the kind of coefficient matrix corresponding to the space variable derivative, and their properties are studied. Necessary and sufficient conditions for stability are obtained in terms of factorization of the transition matrix. The obtained results allow the use of modern algebraic methods for analysis of such systems.

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Convolution algebra representation of systems described by linear hyperbolic partial differential equations

Abstract

All Science Journal Classification (ASJC) codes

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