A convexifying algorithm for the design of structured linear controllers

This paper addresses the design of linear controllers with special structure imposed on the gain matrix. This problem is called a SLC (Structured Linear Control) problem. The SLC problem includes fixed order output feedback control, decentralized control, joint plant and control design, and many other linear control problems. A theoretical framework that allows one to pursue the solution of SLC problems is provided. Although the obtained conditions are nonconvex, it is shown that solving a SLC problem involving standard control objectives such as stability, bounds on the H-2 or H-infinity norms, and real positiveness is not harder than solving a standard unstructured static output feedback problem. A convexifying algorithm that might be used to solve the SLC problem is also developed. At each iteration a certain function is added to the constraints in order to make them convex. At convergence, the artificially introduced convexifying functions reduce to zero, guaranteeing the feasibility of the original problem. Local optimality can be guaranteed. Some examples illustrate how the SLC framework and the convexifying algorithm can improve the solutions of control problem with suboptimal solutions available.