Strict Lyapunov functions for model-reference adaptive control based on the Mazenc construction

We analyze the stability of systems stemming from direct model-reference adaptive control. Although the statements of stability themselves are well-established for many years now, we provide a direct stability analysis both for linear and nonlinear systems under conditions of persistency of excitation. Our proofs are short and constructive as we provide strict Lyapunov functions that have all the required properties as established by Barbashin/Krasovskii's seminal papers on uniform global asymptotic stability.

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