Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear systemthat produces, with a tolerance index ǫ, the same output function when the initial state belongs to a specified set, called ǫ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ǫ-admissible set.

The use of elastic bodies within a multibody simulation became more and more important within the last years. To include the elastic bodies, described as a finite element model in multibody simulations, the dimension of the system of ordinary differential equations must be reduced by projection. For this purpose, in this work, the modal reduction method, a component mode synthesis based method and a moment-matching method are used. Due to the always increasing size of the non-reduced systems, the calculation of the projection matrix leads to a large demand of computational resources and cannot be done on usual serial computers with available memory. In this paper, the model reduction software Morembs++ is presented using a parallelization concept based on the message passing interface to satisfy the need of memory and reduce the runtime of the model reduction process. Additionally, the behaviour of the Block-Krylov-Schur eigensolver, implemented in the Anasazi package of the Trilinos project, is analysed with regard to the choice of the size of the Krylov base, the blocksize and the number of blocks. Besides, an iterative solver is considered within the CMS-based method.

Physical machine systems are represented in the form of differential equations. These differential equations may be of the higher order and difficult to analyses. Therefore, it is necessary to convert the higher-order to lower order which replicates approximately similar properties of the higher-order system (HOS). This article presents a novel approach to reducing the higher-order model. The approach is based on the hunting demeanor of the hawk and escaping of the prey. The proposed method unifies the Harris hawk algorithm and the moment matching technique. The method is applied on single input single output (SISO), multi-input multi-output (MIMO) linear time–invariant (LTI) systems. The proposed method is justified by examining the result. The results are compared using the step response characteristics and response error indices. The response indices are integral square error, integral absolute error, integral time absolute error. The step response characteristics such as rise time, peak, peak time, settling time of the proposed reduced order follows 97%–100% of the original system characteristics.