Probability-one homotopy algorithms for solving the coupled Lyapunov equations arising in reduced-order H-2 /H-infinity modeling, estimation, and control

Optimal reduced-order modeling, estimation, and control with respect to com bined H-2/H-infinity criteria give rise to coupled Lyapunov and Riccati equ ations. To develop reliable numerical algorithms for these problems this pa per focuses on the coupled Lyapunov equations which appear as a subset of t he synthesis equations. In particular, this paper systematically examines t he requirements of probability-one homotopy algorithms to guarantee global convergence, Homotopy algorithms for nonlinear systems of equations constru ct a continuous family of systems and solve the given system by tracking th e continuous curve of solutions to the family. The main emphasis is on guar anteeing transversality for several homotopy maps based upon the pseudogram ian formulation of the coupled Lyapunov equations and variations based upon canonical forms. These results are essential to the probability-one homoto py approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms. (C) 2001 Elsevier Science Inc. A ll rights reserved.