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In time-limited model order reduction, a reduced-order approximation of theoriginal high-order model is obtained that accurately approximates the originalmodel within the desired limited time interval. Accuracy outside that timeinterval is not that important. The error incurred when a reduced-order modelis used as a surrogate for the original model can be quantified in absolute orrelative terms to access the performance of the model reduction algorithm. Therelative error is generally more meaningful than an absolute error because ifthe original and reduced systems' responses are of small magnitude, theabsolute error is small in magnitude as well. However, this does notnecessarily mean that the reduced model is accurate. The relative error in suchscenarios is useful and meaningful as it quantifies percentage errorirrespective of the magnitude of the system's response. In this paper, thenecessary conditions for a local optimum of the time-limited H2 norm of therelative error system are derived. Inspired by these conditions, an obliqueprojection algorithm is proposed that ensures small H2-norm relative errorwithin the desired time interval. Unlike the existing relative error-basedmodel reduction algorithms, the proposed algorithm does not require solutionsof large-scale Lyapunov and Riccati equations. The proposed algorithm iscompared with time-limited balanced truncation, time-limited balancedstochastic truncation, and time-limited iterative Rational Krylov algorithm.Numerical results confirm the superiority of the proposed algorithm over theseexisting algorithms.

Relative Error-based Time-limited H2 Model Order Reduction via Oblique Projection