Brief paper: Linear distributed parameter systems: Closed-loop exponential stability with a finite-dimensional controller

  • Authors:

  • Mark J. Balas

  • Affiliations:

  • Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12181, U.S.A.

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1984

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Abstract

Many engineering systems exhibit dynamical behavior which must be described by partial, rather than ordinary, differential equations. These distributed parameter systems (DPS) have infinite-dimensional state-space descriptions, yet they must be controlled by finite-dimensional feedback systems implemented with a limited number of control actuators and sensors and an on-line digital computer. The most basic problem to be solved is whether such a finite-dimensional controller can produce a stable closed-loop system. In this paper, results are presented which characterize the linear DPS which can be (exponentially) stabilized by a finite-dimensional controller. This characterization makes use of stabilizing subspaces and the solvability of the nonlinear asymmetric Riccati equation. Connections with the usual model reduction approaches to finite-dimensional DPS controller design are also developed.