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

✍ Scribed by Mark J. Balas

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 607 KB
• Volume: 20
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(84)90053-0

✦ Synopsis

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. *