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This paper introduces a new algorithm for reducing large dimensional second-order dynamic systems through the Second Order Arnold Reduction (SOAR) procedure, with a stopping criterion to select an acceptable good order for the reduced model based on a new coefficient called the Numerical- Rank Performance Coefficient (NRPC), for efficient early termination and automatic optimal order selection of the reduced model. The key idea of this method is to calculate the NRPC coefficient for each iteration of the SOAR algorithm and measure the dynamic evolution information of the original system, which is added to each vector of the Krylov subspace generated by the SOAR algorithm. When the dynamical tolerance condition is verified, the iterative procedure of the algorithm stops. Three benchmark models were used as numerical examples to check the effectiveness and simplicity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A comparative study of two important Model Order Reduction (MOR) systems based on internal projections and H 2 norm is presented. It is about Tangential interpolation and the Linear Matrix Inequalities (LMIs) optimisation based methods. In both techniques, the resulting optimal approximants of reduced order are constructed from state space projections and constrained to verify a certain H 2 relative error norm. In this paper, its shown the applicability of these techniques as well for the continuous time as the discrete time multidimensional systems. Since the industry has always been one of the main motivating fields for the development of MOR techniques, the present work offers an expansion to state of the art low order MOR tools and their use to any industrial process to achieve three core features: simplicity of analysis, low computation efforts and an easy and feasible control. [ABSTRACT FROM AUTHOR]

A comparative study based on combined special projections and important frequency-weighted model order reduction (MOR) algorithms to compute optimal approximants for full order digital filters is achieved. It is about the gradient flow (GF) without frequency weighted, the frequency-weighted balanced truncation (FWBT), the GF with frequency weighted (FWGF) and the frequency cross-gramian (CGF) techniques, where special projections of frequency-weighted approximation are used. The obtained low order approximants are expected to follow the original digital filter behavior. With the aim of highlighting the best technique from their implementation, a comparative study is achieved when comparing with a robust MOR technique. Furthermore, two robust performance tools are used namely, the L 2 norm, and the integral-squared error (ISE) allowed to conclude on the efficiency of the best approximation algorithm. [ABSTRACT FROM AUTHOR]

In this paper we present an extension of three important model reduction techniques: namely, the stability equation, the modified pole clustering and the dominant modes methods for conventional (regular) systems to reduce complexity relating to high dimensionality of mathematical models representing physical, generalized (also called singular) systems. Combining these methods to Genetic Algorithms’ tools and exploiting a special representation base where a full order singular system is deflating into proper and improper subsystems, different natures of stable, optimal low order models are obtained. To show the effectiveness of the proposed algorithms, a numerical example is given, where six approximants are derived from a multi-input multi-output singular system. By the use of two optimal norms, the MOR errors are quantified and permits to conclude to the quality of the proposed reduced order models. [ABSTRACT FROM AUTHOR]

Two singular value decomposition (SVD)-based techniques to construct different types of lower degree approximants of a singular system are presented. Such techniques enable preservation of the key properties of the original system, such as stability, and give a quantization of approximation error. The first technique consists of reducing only the proper part of the descriptor system, while the second reduces at once the proper and the improper parts of the system. The numerical results reveal the capabilities of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of the maximum error in model order reduction (MOR) for finite impulse response (FIR) 2‐D digital filter under frequency transformation, which is based on the Roesser state‐space formulation. This study discuss the maximum error obtained from the 2‐D balanced truncation method after and before using the frequency transformation. Several numerical examples are realized to show the invariant of the maximum error in all frequency transformation cases (single variable, two‐variable, and hybrid variable transformations). [ABSTRACT FROM AUTHOR]