STABILITY OF A CLASS OF DIFFERENTIAL EQUATIONS WITH A SINGLE MONOTONE INCREASING NONLINEARITY.

Abstract

The stability of a class of dynamical systems which do not satisfy the Popov theorem is examined. Specifically, by introducing a new Lyapunov function and utilizing frequency domain techniques, sufficient conditions are derived for the stability of the class of systems with a linear plant in the forward path and a monotone increasing nonlinearity in the feedback path. By this assumption of monotone increasing feedback nonlinearities, less restrictive conditions on the linear part of the system, the plant, are obtained. Routh-Hurwitz type conditions are obtained for a class of systems whose linear plants have real, non-zero, zeros. Some examples are presented in order to illustrate the ideas developed. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 28, 1965
Accession Number
AD0467034

Entities

People

  • Charles P. Neuman
  • Kumpati S. Narendra

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Feedback
  • Frequency
  • Frequency Domain
  • Linear Differential Equations
  • Lyapunov Functions
  • Mathematical Analysis
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.