LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov–Krasovskii functionals.

*(English)*Zbl 0974.93060Summary: The author proposes an analogue for linear delay systems of the characterization of asymptotic stability of rational systems by the solvability of an associated Lyapunov equation. It is shown that strong delay-independent stability of a delay system is equivalent to the feasibility of a certain linear matrix inequality (LMI), related to quadratic Lyapunov-Krasovskij functionals.

##### MSC:

93D20 | Asymptotic stability in control theory |

93C23 | Control/observation systems governed by functional-differential equations |

15A39 | Linear inequalities of matrices |

##### Keywords:

linear delay systems; delay-independent stability; quadratic Lyapunov-Krasovskij functionals; linear matrix inequalities; asymptotic stability
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\textit{P. A. Bliman}, Syst. Control Lett. 43, No. 4, 263--274 (2001; Zbl 0974.93060)

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