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Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Moreover, we propose several variants of the error estimator, and compare those variants with the existing ones both theoretically and numerically. It is shown that some of the proposed error estimators perform better than or equally well as the existing ones. All the error estimators considered can be easily extended to estimate the output error of reduced-order modeling for steady linear parametric systems. [ABSTRACT FROM AUTHOR]

Efficient error estimation is important for reliable reduced-order modeling with guaranteed accuracy. We propose an error estimator for reduced-order modeling of linear parametric dynamical systems. The error estimator estimates the error of the reduced transfer function in the frequency domain and can be easily extended to the output error estimation of the reduced-order models (ROMs) for linear steady parametric systems. It is tight and cheap to compute. Using the error estimator, the ROM can be adaptively obtained with high reliability. Numerical results show that the error estimator can accurately estimate the true error even for transfer functions with many resonances. Compared with an existing error bound, the proposed error estimator can be orders of magnitudes sharper and needs much less computational time. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system.Design/methodology/approach The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework.Findings The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time).Originality/value In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method. [ABSTRACT FROM AUTHOR]

The analysis of a posteriori error estimates used in reduced basis methods leads to a model reduction scheme for linear time-invariant systems involving the iterative approximation of the associated error systems. The scheme can be used to improve reduced-order models (ROMs) with initial poor approximation quality at a computational cost proportional to that for computing the original ROM. We also show that the iterative approximation scheme is applicable to parametric systems and demonstrate its performance using illustrative examples. [ABSTRACT FROM AUTHOR]

A fully adaptive model order reduction scheme based on moment matching is proposed to derive the reduced-order models of linear time-invariant (LTI) systems. According to the given error tolerance, the order of the reduced-order model as well as the expansion points for the transfer function is automatically determined on the fly during the process of model reduction. In this sense, the reduced-order model is automatically obtained without assigning the number of moments and expansion points in a priori, which is a prerequisite for the standard implementation of model reduction based on moment matching. The proposed adaptive scheme is found to be efficient when it is tested on various LTI systems. [ABSTRACT FROM AUTHOR]

• The admissibility analysis and robustly passive asynchronous static output feedback control for one sided Lipschitz nonlinear singular Markovian jump systems with uncertainties is addressed for the first time. • Sufficient conditions are derived to guarantee that one sided Lipschitz nonlinear singular Markovian jump systems are regular, impulse free, stochastically stable and have a unique solution with passive performance by using implicit function theorem. • The a synchronous SOF controller, which contains two special cases of mode independence and mode dependence, is designed for the considered system via Linear matrix inequalities. The paper investigates admissibility analysis, the existence and uniqueness (EU) of solutions and robustly passive asynchronous static output feedback (SOF) control for one-sided Lipschitz (OSL) nonlinear singular Markovian jump systems (SMJSs) with uncertainties. Sufficient conditions are derived to guarantee that OSL nonlinear SMJSs are regular, impulse-free, stochastically stable and have a unique solution with passive performance by using implicit function theorem. With these conditions, the design of robust asynchronous SOF controller is presented in form of linear matrix inequality (LMI) constraints. Finally, an example is given to evaluate the operation of our proposed methods. [ABSTRACT FROM AUTHOR]