A trust region method for optimal H2 model reduction

We present a trust-region approach for optimal H
₂
model reduction of multiple-input/multiple-output (MIMO) linear dynamical systems. The proposed approach generates a sequence of reduced order models producing monotone improving H
₂
error norms and is globally convergent to a reduced order model guaranteed to satisfy first-order optimality conditions with respect to H
₂
error criteria. Unlike existing H
₂
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 H
₂
model reduction of MIMO dynamical systems.