Convolution algebra representation of systems described by linear hyperbolic partial differential equations |
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| Authors: | S P Levkov Józef Korbicz |
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| Affiliation: | 1. Academy of Science of UkrSSR, Institute of Cybernetics, prosp , Akad. Glushkova 20, 252-000, Kiev, U.S.S.R;2. Department of Applied Mathematics and Computer Science, ul , Higher College of Engineering , Podgórna 50, 65-246, Zielona Góra, Poland |
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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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