A Trust Region Method for Optimal <i>H</i>₂ 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.