Representation and realization of operational differential equations with time-varying coefficients |
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Authors: | EW Kamen |
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Institution: | School of Electrical Engineering Georgia Institute of Technology, Atlanta, Georgia, USA |
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Abstract: | An algebraic treatment of operational differential equations with time-varying coefficients is presented in terms of skew rings of differential polynomials defined over a Noetherian ring. Included in this framework are delay differential equations with time- varying coefficients. The operator equations are characterized by transfer matrices which are utilized to construct realizations given by first-order vector differential equations with operator coefficients. It is shown that the realization of matrix equations can be reduced to the realization of scalar equations. Finally, a simple procedure is derived for realizing scalar equations. |
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