Root Locations of an Entire Polytope of Polynomials: It Suffices to Check the Edges
Andrew C. Bartlett,Christopher V. Hollot,Huang Lin +2 more
- Iss: 24, pp 1611-1616
TLDR
In this article, the root locations of all polynomials of the entire family can be determined by examining only the roots of the polynomial contained in the exposed edges of the polytope.Abstract:
The presence of uncertain parameters in either a state space or frequency domain description of a linear, time-invariant system manifests itself as variations in the coefficients of the characteristic polynomial. If the family of all such polynomials is polytopic in coefficient space, we'll show that the root locations of the entire family can be completely determined by examining only the roots of the polynomials contained in the exposed edges of the polytope. These results are computationally feasible and this crterion goes beyond the presently available stability tests for uncertain systems by being less conservative in all cases and by explicitly determining all root locations. Equally important is the fact that these results are also applicable to discrete-time systemsread more
Citations
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A generalization of Kharitonov's theorem; Robust stability of interval plants
TL;DR: In this article, a necessary and sufficient condition for the robust stabilization of interval plants is developed, using a generalization of V. L. Kharitonov's theorem (1978).
Journal ArticleDOI
Robust stability for time-delay systems: the edge theorem and graphical tests
TL;DR: In this paper, the robust stability problem for a class of uncertain delay systems where the characteristic equations involve a polytope P of quasi-polynomials (i.e. polynomials in one complex variable and exponential powers of the variable) is discussed.
Journal ArticleDOI
Stability of a polytope of matrices: counterexamples
B.R. Barmish,Minyue Fu,S. Saleh +2 more
TL;DR: In this article, counterexamples illustrate the fundamental differences between polynomial and matrix-stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail.
Journal ArticleDOI
Robust Schur stability of a polytope of polynomials
J.E. Ackermann,B.R. Barmish +1 more
TL;DR: In this paper, the authors provided a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle, which is a discrete-time counterpart for results in S. Bialas (1985) and F.R. Barmish (1987) for continuous case.
Journal ArticleDOI
Computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties
TL;DR: In this paper, a robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices is considered, and a globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented.
References
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Book
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Journal ArticleDOI
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Invariance of the strict Hurwitz property for polynomials with perturbed coefficients
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.
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On the stability properties of polynomials with perturbed coefficients
C. B. Soh,C. Berger,K. Dabke +2 more
TL;DR: In this paper, a method is presented for obtaining the largest hypersphere centered at t = [t 1, t n] containing only polynomials which are stable, where t n is the number of vertices that can be perturbed while preserving the stability properties.
Journal ArticleDOI
Some discrete-time counterparts to Kharitonov's stability criterion for uncertain systems
TL;DR: In this article, the authors gave an elegant and simple stability criterion for continuous-time systems and reported on similar results for discrete-time system, which is similar to the one in this paper.