Determination of the response of a class of nonlinear time invariant systems
This paper illustrates by means of a simple example a new approach for the determination of the time domain response of a class of nonlinear systems. The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first...
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000458 |
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| _version_ | 1832548482095775744 |
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| author | Sudhangshu B. Karmakar |
| author_facet | Sudhangshu B. Karmakar |
| author_sort | Sudhangshu B. Karmakar |
| collection | DOAJ |
| description | This paper illustrates by means of a simple example a new approach for the determination of the time domain response of a class of nonlinear systems. The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional
expansion. Each of the components in the expansion is first transformed into a multidimensional frequency domain and then to a single dimensional frequency domain by the technique of association of variables. By taking into consideration the conditions for the rapid convergence of the functional expansion the response of the system in the frequency domain can effectively be obtained by taking only the first few terms of the expansion. Time domain response is then
found by inverse Laplace transform. |
| format | Article |
| id | doaj-art-9fe088323ca049518dbde8b52641d909 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9fe088323ca049518dbde8b52641d9092025-02-03T06:13:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014361562310.1155/S0161171281000458Determination of the response of a class of nonlinear time invariant systemsSudhangshu B. Karmakar0Western Electric Company, Bell Laboratories, Whippany 07981, New Jersey, USAThis paper illustrates by means of a simple example a new approach for the determination of the time domain response of a class of nonlinear systems. The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional expansion. Each of the components in the expansion is first transformed into a multidimensional frequency domain and then to a single dimensional frequency domain by the technique of association of variables. By taking into consideration the conditions for the rapid convergence of the functional expansion the response of the system in the frequency domain can effectively be obtained by taking only the first few terms of the expansion. Time domain response is then found by inverse Laplace transform.http://dx.doi.org/10.1155/S0161171281000458association of variablesfunctional expansionmultidimensional frequency domainnonlinear impulse responsenonlinear transfer function. |
| spellingShingle | Sudhangshu B. Karmakar Determination of the response of a class of nonlinear time invariant systems International Journal of Mathematics and Mathematical Sciences association of variables functional expansion multidimensional frequency domain nonlinear impulse response nonlinear transfer function. |
| title | Determination of the response of a class of nonlinear time invariant systems |
| title_full | Determination of the response of a class of nonlinear time invariant systems |
| title_fullStr | Determination of the response of a class of nonlinear time invariant systems |
| title_full_unstemmed | Determination of the response of a class of nonlinear time invariant systems |
| title_short | Determination of the response of a class of nonlinear time invariant systems |
| title_sort | determination of the response of a class of nonlinear time invariant systems |
| topic | association of variables functional expansion multidimensional frequency domain nonlinear impulse response nonlinear transfer function. |
| url | http://dx.doi.org/10.1155/S0161171281000458 |
| work_keys_str_mv | AT sudhangshubkarmakar determinationoftheresponseofaclassofnonlineartimeinvariantsystems |