Convex l_2 Synthesis for Multidimensional Systems

This paper deals with the design of control systems for multidimensional systems in the Roesser state space format with an l2 induced gain performance criterion. The region of analyticity of the closed loop system can be pre-specified, corresponding to the relaxation of the standard causality requirement (or equivalently, stability requirement) found in H-infinity optimization. These techniques may be used for designing spatially distributed controllers for spatially distributed systems. The main technical contribution of the paper is the extension of the synthesis results of Packard and of Apkarian and Gahinet to non-definite scalings. The solution to the problem takes the form of a linear matrix inequality.