Globally Convergent Homotopy Algorithms for the Combined H-squared/ H-to Infinity Model Reduction Problem

The problem of finding a reduced order model, optimal in the H-squared sense, to a given system model is a fundamental one in control system analysis and design. The addition of a H-to infinity constraint to the H-squared optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probablity-one homotopy methods the combined H-squared/H-to infinity model reduction problem is difficult to solve. Several approaches based on homotopy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations -- input normal, Ly, Bryson, and Cannon's 2 x 2 block parametrization -- are developed and compared here.