A trust region method for optimal H2 model reduction

We present a trust-region approach for optimal H₂ model reduction of multiple-input/multiple-output (MIMO) linear dynamical systems. The proposed approach generates a sequence of reduced order models producing monotone improving H₂ error norms and is globally convergent to a reduced order model guaranteed to satisfy first-order optimality conditions with respect to H₂ error criteria. Unlike existing H₂ descent methods, the method does not require solving any Lyapunov equations and is both numerically stable and computationally tractable even for very large order systems. This method appears to be the first descent approach that uses Hessian information for optimal H₂ model reduction of MIMO dynamical systems.