H2 Optimal Model Order Reduction Over a Finite Time Interval

For a time-limited H
₂
cost function defined over a finite time interval, we obtain analytical expressions of the gradients using a gramian framework. The time-limited H
₂
optimal model reduction problem is non-convex. In order to solve the optimization problem, we substitute the gradients in a standard quasi-Newton solver. The method obtains local minimizers of the time-limited H
₂
cost function.