Convergence of Trajectories for a Controlled Viscous Burgers’ Equation

  • Christopher I. Byrnes
  • David S. Gilliam
  • Victor I. Shubov
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 118)


In this paper we consider a boundary control problem for Burgers’ equation on a finite interval. The controls enter as gain parameters in the boundary conditions as in [1, 2]. The uncontrolled problem is obtained by equating the control parameters to zero while the zero dynamics system is obtained by equating the control parameters to infinity, or (intuitively) as the “high gain limit” of the system as the gains approach plus infinity. The main result of the paper is a nonlinear enhancement of the classical root locus result which states that the trajectories of the closed loop system converge to the trajectories of the zero dynamics system as the gains are increased to infinity.

1991 Mathematics Subject Classification

93B05 93B28 93B52 

Key words and phrases

Boundary control nonlinear distributed parameter systems zero dynamics convergence of trajectories 


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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Christopher I. Byrnes
    • 1
  • David S. Gilliam
    • 2
  • Victor I. Shubov
    • 2
  1. 1.Department of Systems Science and MathematicsWashington UniversitySt. LouisUSA
  2. 2.Department of MathematicsTexas Tech UniversityLubbockUSA

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