Topic
Hurwitz matrix
About: Hurwitz matrix is a research topic. Over the lifetime, 441 publications have been published within this topic receiving 6986 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: Some fundamental insights into observer design for the class of Lipschitz nonlinear systems are presented and a systematic computational algorithm is presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability.
Abstract: This paper presents some fundamental insights into observer design for the class of Lipschitz nonlinear systems. The stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix. The correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented. These conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix. The eigenvalues have to be located sufficiently far out into the left half-plane, and the eigenvectors also have to be sufficiently well-conditioned for ensuring asymptotic stability. Based on these results, a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability.
913 citations
TL;DR: In this article, the authors derived a set of differential equations for the eigenvalues and eigenvectors of the stability matrix of a dynamical system, as well as for the Lyapunov exponents and the corresponding eigenvector.
337 citations
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TL;DR: In this paper, a new approach via Hurwitz numbers to Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of curves is presented.
Abstract: The main goal of the paper is to present a new approach via Hurwitz numbers to Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of curves. A secondary goal is to present an exposition of the circle of ideas involved: Hurwitz numbers, Gromov-Witten theory of the projective line, matrix integrals, and the theory of random trees. Further topics will be treated in a sequel.
311 citations
TL;DR: It is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a Hurwitz matrix.
Abstract: This note addresses the stability problem of continuous-time positive systems with time-varying delays. It is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a Hurwitz matrix. The result is a time-varying version of the widely-known asymptotic stability criterion for constant-delay positive systems. A numerical example illustrates the correctness of our result.
282 citations
TL;DR: In this article, a theorem of Kharitonov is exploited to obtain a general result for polynomials of any degree for systems with n \leq 4, where the maximal intervals of the coefficients are given in a recent paper by Guiver and Bose.
Abstract: Given a strictly Hurwitz polynomial f(\lambda) = \lambda^{n} + a_{n-1} \lambda^{n-1} + a_{n-2}\lambda^{n-2}+...+ a_{1}\lambda + a_{0} , it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict Hurwitz property. For systems with n \leq 4 , maximal intervals of the a i are given in a recent paper by Guiver and Bose [1]. In this note, a theorem of Kharitonov is exploited to obtain a general result for polynomials of any degree.
236 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2024 | 1 |
| 2023 | 6 |
| 2022 | 29 |
| 2021 | 6 |
| 2020 | 7 |