Foundations of Feedback Theory for Nonlinear Dynamical Systems

Abstract

We study the fundamental properties of feedback for nonlinear, time- varying, multi-input, multi-output, distributed systems. The classical Black formula is generalized to the nonlinear case. Achievable advantages and limitations of feedback in nonlinear dynamical systems are classified and studied in five categories: desensitization, disturbance attenuation, linearizing effect, asymptotic tracking and disturbance attenuation, linearizing effect, asymptotic tracking and disturbance rejection, stabilization. Conditions under which feedback is beneficial for nonlinear dynamical systems are derived. Our results show that if the appropriate linearized inverse return difference operator is small, then the nonlinear feedback system has advantages over the open-loop system. Several examples are provided to illustrate the results.

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Document Details

Document Type
Technical Report
Publication Date
Aug 31, 1979
Accession Number
ADA086578

Entities

People

  • C. A. Desoer
  • Y. T. Wang

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aircrafts
  • Amplifiers
  • Attenuation
  • Banach Space
  • Closed Loop Systems
  • Control Systems
  • Electron Tubes
  • Feedback
  • Feedback Amplifiers
  • Frequency Bands
  • Linear Systems
  • Measuring Instruments
  • Nonlinear Systems
  • Open Loop Systems
  • Rejection
  • Steady State
  • Transfer Functions

Readers

  • Control Systems Engineering.
  • Theoretical Analysis.