Accession Number : AD0677029

Title :   EXPONENTIAL FUNCTION SETS IN THE ANALYSIS OF NONLINEAR SYSTEMS.

Descriptive Note : Technical rept.,

Corporate Author : SYRACUSE UNIV N Y DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Kirwin,Gerald James

Report Date : SEP 1968

Pagination or Media Count : 97

Abstract : 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)

Descriptors :   (*CONTROL SYSTEMS, NONLINEAR SYSTEMS), (*INFORMATION THEORY, CONTROL SYSTEMS), EXPONENTIAL FUNCTIONS, TRANSFER FUNCTIONS, NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRAL TRANSFORMS, FUNCTIONAL ANALYSIS, HARMONIC ANALYSIS, PERIODIC VARIATIONS, NUMERICAL ANALYSIS, APPROXIMATION(MATHEMATICS), TRANSIENTS, THESES

Subject Categories : Theoretical Mathematics
      Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE