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Worst Exponential Decay Rate for Degenerate Gradient flows subject to persistent excitation

Abstract : In this paper we estimate the worst rate of exponential decay of degenerate gradient flows (x) over dot = -Sx, issued from adaptive control theory. Under persistent excitation assumptions on the positive semidefinite matrix S, we provide upper bounds for this rate of decay consistent with previously known lower bounds and analogous stability results for more general classes of persistently excited signals. The strategy of proof consists in relating the worst decay rate to optimal control questions and studying in detail their solutions. As a by-product of our analysis, we also obtain estimates for the worst L-2-gain of the time-varying linear control systems (x) over dot = -cc(inverted perpendicular) x + u, where the signal c is persistently excited, thus solving an open problem posed by Rantzer in 1999.
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https://hal.archives-ouvertes.fr/hal-02792435
Contributor : Dario Prandi Connect in order to contact the contributor
Submitted on : Friday, June 5, 2020 - 8:45:11 AM
Last modification on : Sunday, June 26, 2022 - 2:50:34 AM

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Paolo Mason, Yacine Chitour, Dario Prandi. Worst Exponential Decay Rate for Degenerate Gradient flows subject to persistent excitation. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, In press, 59 (4), pp.3040-3067. ⟨10.1137/20M1343427⟩. ⟨hal-02792435⟩

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