AN ALGEBRAIC APPROACH TO THE CONTROL OF SPATIALLY DISTRIBUTED SYSTEMS — THE 2-D SYSTEMS CASE WITH A PHYSICAL APPLICATION

In this paper we develop new results on control systems design for spatially distributed linear systems using an n-D systems approach. The basic ideas are explained using as an example heat conduction in a rod where the measurements and control action applied are based on an array of sensors and heaters. The first part of the analysis given shows how the process dynamics for this case can be approximately described by a 2-D transfer function, i.e. a fraction of two bivariate polynomials. This is followed by stability analysis and tests. Finally, a Youla-Kucera parametrization of all stabilizing controllers is used to develop a simple design procedure for H2-optimal control laws.