Book ChapterDOI
Realization and Interpolation of Rational Matrix Functions
Joseph A. Ball,Israel Gohberg,Leiba Rodman +2 more
- pp 1-72
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This paper generalize for matrix valued functions a number of well known interpolation problems for scalar rational functions and obtain explicit formulas for the solutions and gives a more systematic and transparent exposition based exclusively on analysis in finite dimensional spaces.Abstract:
In this paper we generalize for matrix valued functions a number of well known interpolation problems for scalar rational functions and obtain explicit formulas for the solutions The realization approach toward the study of rational matrix functions from systems theory serves here as the main tool The main results recently appeared in the literature; here we give a more systematic and transparent exposition based exclusively on analysis in finite dimensional spacesread more
Citations
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Journal ArticleDOI
On the solution of the minimal rational interpolation problem
TL;DR: In this article, it was shown that reachability and observability indices of appropriately defined pairs of matrices provide the key for solving the minimal rational (bitangen- tial) interpolation problem.
Journal ArticleDOI
Minimization of the maximum peak-to-peak gain: the general multiblock problem
TL;DR: A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented and further insight is gained into the structure of the optimal solution.
Book ChapterDOI
Interpolation problems, extensions of symmetrical operators and reproducing kernel spaces ii
TL;DR: In this paper, the authors studied interpolation problems for pairs of matrix functions of the extended Nevanlinna class using two different approaches and made explicit the various links between them.
Proceedings ArticleDOI
Factorization of nonlinear systems: toward a theory for nonlinear H/sup infinity / control
J.A. Ball,J.W. Helton +1 more
TL;DR: A natural approach to H/sup infinity / control for nonlinear systems, by developing a theory of factorization for a nonlinear time-invariant causal map, is presented in this paper.
Journal ArticleDOI
Inner-outer factorization of nonlinear operators
Joseph A. Ball,J. William Helton +1 more
TL;DR: In this article, the Stein equation is extended to the setting of input-output maps of nonlinear discrete-time systems, and a particaular computable class of examples is presented for illustration.
References
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Journal ArticleDOI
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.
Book
A Course in H∞ Control Theory
TL;DR: In this paper, the standard problem and performance bounds of model-matching theory are discussed. But the performance bounds are not defined. And they are not considered in this paper.