Journal ArticleDOI
Characterization of the solution to the optimal H∞ model reduction problem
Davut Kavranoglu,Maamar Bettayeb +1 more
TLDR
In this article, the authors studied the H ∞ norm approximation of a given stable, proper, rational transfer function by a lower order stable proper transfer function and developed a simple characterization of the solution to the optimal model reduction problem.About:
This article is published in Systems & Control Letters.The article was published on 1993-02-01. It has received 96 citations till now. The article focuses on the topics: Hankel singular value & Norm (mathematics).read more
Citations
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Journal ArticleDOI
Model Reduction by Moment Matching for Linear and Nonlinear Systems
TL;DR: A re-visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment that is used to pose and solve the model reduction problem by moment matching for nonlinear systems.
Model Reduction of Multi-Dimensional and Uncertain Systems
TL;DR: In this paper, the authors present model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation (LFT) on a repeated scalar uncertainty structure, which can be interpreted either as doing state order reduction for multi-dimensional systems, or as uncertainty simplification in the case of uncertain systems.
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Model reduction of multidimensional and uncertain systems
TL;DR: Model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation on a repeated scalar uncertainty structure and a related necessary and sufficient condition for the exact reducibility of stable uncertain systems are presented.
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H∞ model reduction of Markovian jump linear systems☆
TL;DR: It is shown that the reduced order models exist if a set of matrix inequalities is feasible, and an effective iterative algorithm involving linear matrix inequalities are suggested to solve the matrix inequalities characterizing the model reduction solutions.
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Improved lmi conditions for gain scheduling and related control problems
TL;DR: In this article, the realness of the parameters is exploited using a "skew-symmetric scaling" technique, which can be applied to other problems such as anti-windup control, nonlinear control and model reduction.
References
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Journal ArticleDOI
Principal component analysis in linear systems: Controllability, observability, and model reduction
TL;DR: In this paper, it is shown that principal component analysis (PCA) is a powerful tool for coping with structural instability in dynamic systems, and it is proposed that the first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.
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All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†
TL;DR: In this paper, a complete characterization of all rational functions that minimize the Hankel-norm is derived, and the solution to the latter problem is via results on balanced realizations, all-pass functions and the inertia of matrices, all in terms of the solutions to Lyapunov equations.
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Optimal Hankel-norm model reductions: Multivariable systems
Sun-Yuan Kung,David W. Lin +1 more
TL;DR: In this paper, a Hankel-norm optimal solution for multivariable system reduction problems is presented, with the optimality verified by a complete error analysis, based on the scalar ease approach.
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