A new approach for frequency weightedL2 model reduction of discrete-time systems

Diab, Mohamad O.; Liu, W.Q.; Sreeram, Victor

doi:10.1002/(sici)1099-1514(199805/06)19:3<147::aid-oca623>3.0.co;2-o

Cited by 16 publications

(1 citation statement)

References 10 publications

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“…Enns (1984) and Wang et al (1999) and many others have used the H 1 norm. The H 2 norm was used by Spanos et al (1992) and Diab et al (1998), just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Model reduction of bilinear systems described by input–output difference equation

Al-Baiyat¹

2004

International Journal of Systems Science

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A class of single input single output bilinear systems described by their input-output difference equation is considered. A simple expression for the Volterra kernels of the system is derived in terms of the coefficients of difference equation. An algorithm, based on the singular value decomposition of a generalized Hankel matrix, is also developed. The algorithm is then used to find a reduced-order bilinear state-space model. The Hankel approach will be extensively studied under different data length cases and different orders of the state-space models. A numerical example is presented to illustrate the effectiveness of the proposed algorithm.

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“…Enns (1984) and Wang et al (1999) and many others have used the H 1 norm. The H 2 norm was used by Spanos et al (1992) and Diab et al (1998), just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Model reduction of bilinear systems described by input–output difference equation

Al-Baiyat¹

2004

International Journal of Systems Science

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Model reduction of discrete Markovian jump systems with time‐weighted H₂ performance

Sun

Lam²

2015

Intl J Robust & Nonlinear

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This paper is concerned with the optimal time-weighted H 2 model reduction problem for discrete Markovian jump linear systems (MJLSs). The purpose is to find a mean square stable MJLS of lower order such that the time-weighted H 2 norm of the corresponding error system is minimized for a given mean square stable discrete MJLSs. The notation of time-weighted H 2 norm of discrete MJLS is defined for the first time, and then a computational formula of this norm is given, which requires the solution of two sets of recursive discrete Markovian jump Lyapunov-type linear matrix equations. Based on the time-weighted H 2 norm formula, we propose a gradient flow method to solve the optimal time-weighted H 2 model reduction problem. A necessary condition for minimality is derived, which generalizes the standard result for systems when Markov jumps and the time-weighting term do not appear. Finally, numerical examples are used to illustrate the effectiveness of the proposed approach.M. SUN AND J. LAM where x.k/ 2 R n represents the state variable of the system, u.k/ 2 R p is the control input vector, and´.k/ 2 R m is the output. The parameter Â.k/ stands for the state of a Markov

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H2 order-reduction for bilinear systems based on Grassmann manifold

Xu¹,

Jiang²,

Yang³

2015

Journal of the Franklin Institute

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A new approach for frequency weightedL2 model reduction of discrete-time systems

Cited by 16 publications

References 10 publications

Model reduction of bilinear systems described by input–output difference equation

Model reduction of bilinear systems described by input–output difference equation

Model reduction of discrete Markovian jump systems with time‐weighted H₂ performance

H2 order-reduction for bilinear systems based on Grassmann manifold

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A new approach for frequency weightedL2 model reduction of discrete-time systems

Cited by 16 publications

References 10 publications

Model reduction of bilinear systems described by input–output difference equation

Model reduction of bilinear systems described by input–output difference equation

Model reduction of discrete Markovian jump systems with time‐weighted H2 performance

H2 order-reduction for bilinear systems based on Grassmann manifold

Contact Info

Product

Resources

About

Model reduction of discrete Markovian jump systems with time‐weighted H₂ performance