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**Root locations of an entire polytope of polynomials: It suffices to check the edges.**
*(English)*
Zbl 0652.93048

Summary: The presence of uncertain parameters in a state space or frequency domain description of a linear, time-invariant system manifests itself as variability in the coefficients of the characteristic polynomial. If the family of all such polynomials is polytopic in coefficient space, we show that the root locations of the entire family can be completely determined by examining only the roots of the polynomials contained in the explosed edges of the polytope. These procedures are computationally tractable, and this criterion improves upon the presently available stability tests for uncertain systems, being less conservative and explicitly determining all root locations. Equally important is the fact that the results are also applicalbe to discrete-time systems.

### MSC:

93D99 | Stability of control systems |

93C05 | Linear systems in control theory |

30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |

52Bxx | Polytopes and polyhedra |

### Keywords:

linear, time-invariant system; root locations; polytope; stability tests; uncertain systems; time-invariant
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\textit{A. C. Bartlett} et al., Math. Control Signals Syst. 1, No. 1, 61--71 (1988; Zbl 0652.93048)

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### References:

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