Convex and finite-dimensional conditions for controller synthesis with dynamic integral constraints

In this paper, the problem of synthesizing controllers when the allowable disturbances and the cost criterion are defined via a finite number of matrix valued dynamic integral constraints, is solved. This allows one to design optimal control systems for plants subject to fixed-input disturbances (such as steps, sinusoids, and periodic disturbances), disturbances of fixed and known spectrum, disturbances defined as the set of signals in the kernel of a given operator, and combinations thereof, to penalize particular frequency components of the error variables in the control design process, to penalize the maximum amplitude of an error variable, and to consider other general cost criteria in the optimization, and to solve a large class of robust control synthesis problems. Necessary and sufficient conditions for the general problem to have a solution are in terms of a computationally attractive, finite dimensional linear matrix inequality.