![]() ![]() ![]() Besides reviewing existing methods and the computational techniques needed to implement them, open issues are discussed, and some new results are proposed. Arch Comput Methods Eng 15(3):229–275, 2008) which we do not consider here. This complements recent surveys on generating reduced-order models for parameter-dependent problems (Benner et al. In this survey paper, we review some popular MOR methods for linear and nonlinear large-scale dynamical systems, mainly used in electrical and control engineering, in computational electromagnetics, as well as in micro- and nano-electro-mechanical systems design. Wide applications of MOR have been found not only in simulation, but also in optimization and control. Recently, MOR has been intensively further developed for increasingly complex dynamical systems. In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and wide applicability for simulating large-scale mathematical models in engineering and the sciences. Finally, numerical experiments are employed to substantiate the effectiveness of the presented algorithms. In addition, we also carried out a correlation analysis on the stability of improved algorithms. To alleviate the inadequacies of this approach, we have improved the model reduction procedure, which is based upon the dominant subspace projection method. For this approach, there is a disadvantage that unstable systems may be generated although the original one is stable. In order to achieve the purpose of model order reduction, the states with smaller singular values are then truncated, so as to further obtain the reduced order model. After that, the approximate balanced system of the K-power bilinear system is constructed by the corresponding projection transformation of each subsystem. The method first aims to rewritten the K-power bilinear system as a general bilinear system and calculate the approximate low-rank factors of the cross Gramian of the bilinear system by combining the idea of Laguerre functions expansion of the matrix exponential function. This paper presents a series of structure-preserving model order reduction algorithms for K-power bilinear systems via Laguerre functions. ![]()
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