Determination of the response of a class of nonlinear time invariant systems

• Main Author: Sudhangshu B. Karmakar
• Format: Article
• Language: English
• Published: Hindawi Limited 1981-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: association of variables; functional expansion; multidimensional frequency domain; nonlinear impulse response; nonlinear transfer function.
• Online Access: http://dx.doi.org/10.1155/S0161171281000458
• ISSN: 0161-1712; 1687-0425

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.