Fixed-architecture controller synthesis for systems with input-output time-varying nonlinearities

Wassim M. Haddad, Vikram Kapila

Research output: Contribution to journalArticle

Abstract

In this paper we develop a fixed-architecture controller analysis and synthesis framework that addresses the problem of multivariable linear time-invariant systems subject to plant input and plant output time-varying nonlinearities while accounting for robust stability and robust performance over the allowable class of nonlinearities. The proposed framework is based on the classical Lure problem and the related Aizerman conjecture concerning the stability of a feedback loop involving a sector-bounded nonlinearity. Specifically, we extend the classical notions of absolute stability theory to guarantee closed-loop stability of multi variable systems in the presence of input nonlinearities. In order to capture closed-loop system performance we also consider the minimization of a quadratic performance criterion over the allowable class of input nonlinearities. Our approach is directly applicable to systems with saturating actuators and provides full and reduced-order dynamic compensators with a guaranteed domain of attraction. The principal result is a set of constructive sufficient conditions for absolute stabilization characterized via a coupled system of algebraic Riccati and Lyapunov equations. The effectiveness of design approach is illustrated by several numerical examples.

Original languageEnglish (US)
Pages (from-to)675-710
Number of pages36
JournalInternational Journal of Robust and Nonlinear Control
Volume7
Issue number7
StatePublished - Jul 1997

Fingerprint

Time-varying
Nonlinearity
Synthesis
Controller
Controllers
Output
Multivariable systems
Closed loop systems
Actuators
Stabilization
Absolute Stability
Lyapunov Equation
Algebraic Riccati Equation
Multivariable Systems
Robust Performance
Domain of Attraction
Feedback
Stability Theory
Feedback Loop
Compensator

Keywords

  • Domains of attraction
  • Fixed-architecture control
  • Gain and phase margins
  • Saturating controls

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

Fixed-architecture controller synthesis for systems with input-output time-varying nonlinearities. / Haddad, Wassim M.; Kapila, Vikram.

In: International Journal of Robust and Nonlinear Control, Vol. 7, No. 7, 07.1997, p. 675-710.

Research output: Contribution to journalArticle

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