EXPONENTIAL FUNCTION SETS IN THE ANALYSIS OF NONLINEAR SYSTEMS.
SYRACUSE UNIV N Y DEPT OF ELECTRICAL ENGINEERING
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An approximate solution for the response of the system to a transient i.e., nonperiodic input signal is proposed. The systems under consideration are single loop control systems having a linear dynamic subsystem in tandem in the loop with a memory-free nonlinear subsystem. An approximating system is devised by replacing each signal with its projection on a subspace of square-integrable functions. The transmission of signals in the subspace through the nonlinear part of the system is expressed by a multidimensional equivalent gain function. Several examples are presented in which the new technique is used to generate approximate solutions when the linear subsystem is of second or third order and the nonlinear subsystem is characterized by a polynomial input-output relation. The approximate response is compared with the solution resulting from a numerical integration of the actual system equations. Author
- Theoretical Mathematics