Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

Abstract

Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.

Factorization‐based frequency‐weighted optimal Hankel‐norm model reduction

“…A similar realization dependent modification of [18] is presented in [19] to reduce the approximation error. Later, Imran et al [20] presented an improvement of [11] by considering a similar effect on the eigenvalues of symmetric matrices. Some recent developments on model reduction are appeared in [21][22][23][24][25].…”

“…It is shown that the transformation of the original system into a new realization is non-unique by including variations of both algorithms using an additional factorization. It is observed that both proposed algorithms and their variations give a lower approximation error than [9,[11][12][13]17,19,20]. The advantages of the proposed algorithms are as follows: (i) assuring the stability of reduced model in case of single-and double-sided weights; (ii) availability of easily computable error bound; and (iii) easily extendable to discrete-time systems.…”

Model reduction of discrete-time systems in limited intervals

“…The use of input-, output-, or both-sided frequency weighting is possible; however, guaranteed stable reduced-order models (ROMs) are only achieved in the single-sided case [9]. Several modifications in [9] to guarantee stability have been presented in the literature [10][11][12][13].…”

Finite-frequency model order reduction of discrete-time linear time-delayed systems

“…Model order reduction is an indispensable tool to generate simpler reduced model while sacrificing some accuracy [1]. The commonly used model order reduction approaches include Krylov-subspace projection method [2], balanced truncation method [3,4], modal truncation method [5] and numerical optimization methods [6].…”

“…Regarding the frequency-domain approximation performance, the existing techniques generally tried to minimize the approximate error over the entire frequency range. For many practical model order reduction problems, it has been pointed out that the requirement on the approximation accuracy over some prespecified frequency range is more important than that beyond the frequency range [3,4,9,10,[34][35][36]. Therefore, it is more appealing to further improve the approximation performance over the concerned frequency ranges meanwhile ignoring the approximation performance over the rest frequency parts.…”