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In this paper, we obtain the functional derivatives of a finite horizon errornorm between a full-order and a reduced-order continuous-time lineartime-varying (LTV) system. Based on the functional derivatives, first-ordernecessary conditions for optimality of the error norm are derived, and aprojection-based iterative scheme for model reduction is proposed. Theiterative scheme upon convergence produces reduced-order models satisfying theoptimality conditions. Finally, through a numerical example, we demonstrate thebetter performance of the proposed model reduction scheme in comparison to thefinite horizon balanced truncation algorithm for continuous-time LTV systems.

An iterative scheme for finite horizon model reduction of continuous-time linear time-varying systems