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Stability results for point time-delay systems obtained via Rouche’s theorem. (English) Zbl 1069.93035

The maximum modulus principle and the Rouché theorem on zeros of analytic functions in complex domains are used to derive sufficient conditions for stability of a continuous-time linear dynamical system affected by constant time-delay, or equivalently for stability of a quasipolynomial. The conditions, proposed in Theorem 1, are expressed in the frequency domain. They consist in checking whether a univariate polynomial is globally positive. The conditions are then relaxed in various ways, leading to more restrictive algebraic criteria. Finally, the results are extended to stabilization via linear state or output feedback.

MSC:

93D20 Asymptotic stability in control theory
93C80 Frequency-response methods in control theory
93C23 Control/observation systems governed by functional-differential equations
93D15 Stabilization of systems by feedback
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