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Model Reduction of Large Scale Descriptor Systems Using Time Limited Gramians

A new technique for model order reduction of large scale continuous linear time invariant descriptor systems in limited time interval is proposed. The concept of time limited Gramians for descriptor systems is introduced for applications involving analysis, design or optimization in specific time interval. Balanced truncation based on magnitudes of Hankel singular values of the computed Gramians is performed to obtain the reduced order models in limited time interval. An approximate solution of time limited projected Lyapunov equations is developed and Cholesky factorisation of time limited Gramians is performed. Moreover, stability conditions for reduced order system are stated and two algorithms for stability preservation of reduced order models are presented. Results certify the successful application of the proposed techniques.