Optimal triangular approximation for linear stable multivariable systems

D. A. Oyarzun, M. E. Salgado

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

This paper deals with the problem of obtaining a stable triangular approximation for a linear, square, stable, discrete-time MIMO system. We solve this problem through an analytic procedure that yields an explicit solution of a convex optimization problem. The optimized quantity is the L2 norm of the relative modelling error. An interesting feature of the proposed methodology is that, if the MIMO system has nonminimum phase zeros near the stability boundary, then the derived approximation has, at least, a set of zeros close to them. The usefulness of our result comes mainly from its use as nominal model in triangular controller design procedures based on a triangular plant model.
Original languageEnglish
Title of host publication2007 American Control Conference
Number of pages6
Publication statusPublished - 1 Jul 2007
Event2007 American Control Conference - New York City, United States
Duration: 11 Jul 200713 Jul 2007


Conference2007 American Control Conference
Abbreviated titleACC 2007
Country/TerritoryUnited States
CityNew York City
Internet address

Keywords / Materials (for Non-textual outputs)

  • approximation theory
  • control system synthesis
  • convex programming
  • discrete time systems
  • linear systems
  • MIMO systems
  • poles and zeros
  • stability
  • optimal triangular approximation
  • linear stable multivariable systems
  • square system
  • discrete-time system
  • MIMO system
  • convex optimization problem
  • nonminimum phase zero
  • stability boundary
  • triangular controller design
  • triangular plant model
  • Linear approximation
  • MIMO
  • Optimal control
  • Control systems
  • Stability
  • Filtering theory
  • Cities and towns
  • Vehicles
  • Design optimization
  • Reduced order systems


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