A Homotopy Algorithm for Solving the Optimal Projection Equations for Fixed-Order Dynamic Compensation: Existence, Convergence and Global Optimality

The purpose of this paper is to present a homotopy algorithm for solving the Optimal Projection Equations. Questions of existence and the number of solutions will also be examined. It will be shown that the number of stabilizing solutions to the given Optimal Projection Equations can be determined and that all solutions can be computed via a homotopic continuation from a simple problem. For an important special case, where the number of inputs or the number of outputs to the system is less than or equal to the dimension of the compensator, there is only one solution to the OPE, thus guaranteeing that globally optimum reduced order controller can be computed.