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.
A new scheme for model order reduction of large-scale second-order systems in time-limited intervals is presented. Time-limited Gramians that are solutions of continuous-time algebraic Lyapunov equations for second-order form systems are introduced. Time-limited second-order balanced truncation procedures with provision of balancing position and velocity Gramians are formulated. Stability conditions for reduced-order models are stated and algorithms that preserve stability in reduced-order models are discussed. Numerical examples are presented to validate the superiority of the proposed scheme compared with the infinite-time Gramians technique for time-limited applications.
The present study confirms the significant involvement of P2X receptors in the immune responses mediated by the PBMCs in the chronic HCV infection, which should be further investigated to devise strategies to augment the immune system against this chronic viral disease.
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