Synthesis of fixed-structure controllers via numerical optimization

We propose an iterative algorithm for designing linear time-invariant controllers with some prespecified structure. The iterations require the solution of optimization problems based on linear matrix inequalities, in which either the Lyapunov function proving a certain property or the controller to be designed is alternately regarded as the optimization variable (while the other is fixed). A number of structure constraints on the controller (reduced-order, decentralized, etc.) can be addressed using this technique, which also extends to plants with nonlinearities or uncertainties. The algorithm is heuristic in nature, and is not guaranteed to converge globally. However it provides a locally optimal solution which depends on the initialization of the algorithm, and serves as a useful design tool