Feedback control of LTI spatially distributed systems: an input-output approach

Explores an input-output approach to distributed systems which takes account of the spatially distributed nature of a system´s input and output signals. The approach is a generalization of H^∞ control in the sense that the 2-norm is used for both the space- and time-dependence of signals. We consider the basic theory of systems and representations as well as issues of approximation and robust control. We introduce the class of finite-dimensional, distributed, linear, time-invariant (FDDLTI) systems which defines both a particular type of finite-dimensional approximation of spatially distributed plants and a structure for spatially distributed controllers. Our approach to controller design treats sensors and actuators as part of the controller rather than as part of the plant. As a consequence, optimal controller design involves the computation of the optimal locations and shapes of the spatial distribution functions of the sensors and actuators as well as an optimal (lumped) controller transfer matrix connecting the optimally placed and shaped sensors and actuators. On the basis of FDDLTI systems we propose two controller synthesis methods similar to the standard H^∞-synthesis techniques of “H^∞ loop-shaping” and “μ-synthesis”