Journal ArticleDOI
All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†
Reads0
Chats0
TLDR
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.Abstract:
The problem of approximating a multivariable transfer function G(s) of McMillan degree n, by Ĝ(s) of McMillan degree k is considered. A complete characterization of all approximations that minimize the Hankel-norm is derived. The solution involves a characterization of all rational functions Ĝ(s) + F(s) that minimize where Ĝ(s) has McMillan degree k, and F(s) is anticavisal. 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. It is then shown that where σ k+1(G(s)) is the (k+l)st Hankel singular value of G(s) and for one class of optimal Hankel-norm approximations. The method is not computationally demanding and is applied to a 12-state model.read more
Citations
More filters
Journal ArticleDOI
State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Book
Essentials of Robust Control
Kemin Zhou,John Doyle +1 more
TL;DR: In this article, the authors introduce linear algebraic Riccati Equations and linear systems with Ha spaces and balance model reduction, and Ha Loop Shaping, and Controller Reduction.
Book
Optimal Control: Linear Quadratic Methods
TL;DR: In this article, an augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems, with step-by-step explanations that show clearly how to make practical use of the material.
Proceedings ArticleDOI
State-space solutions to standard H 2 and H ∞ control problems
TL;DR: In this article, simple state-space formulas are presented for a controller solving a standard H∞-problem, where the controller has the same state-dimension as the plant, its computation involves only two Riccati equations, and it has a separation structure reminiscent of classical LQG theory.
Book
Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools
TL;DR: This book is to introduce basic model-based FDI schemes, advanced analysis and design algorithms and the needed mathematical and control theory tools at a level for graduate students and researchers as well as for engineers.
References
More filters
Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book
Optimization by Vector Space Methods
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
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.