Matrosov theorem for parameterized families of discrete-time systems
The theorem for parametrized discrete-time time-varying systems is a discrete-time version of the continuous-time result in [\textit{A. Loria, E. Panteley, D. Popović} and \textit{A. R. Teel}, ``\(\delta\)-persistency of excitation: A necessary and sufficient condition for uniform attractivity''. In: Proceedings of the 41st Conference on Decision and Control, Las Vegas, Nevada, USA, 3506--3511 (2002)]. The result facilitates controller design for sampled-data nonlinear systems via their approximate discrete-time models. An application of the theorem to establishing uniform asymptotic stability of systems controlled by model reference adaptive controllers designed via approximate discrete-time plant models is presented. Remark. In continuous case of system \(x(k+1) = F_T(k,x(k))\) the condition similar to condition (b) of Theorem 1 was used in the paper [\textit{A. A. Martynyuk} and \textit{A. Yu. Obolensky}, Differ. Equations 16, 890--910 (1981; Zbl 0527.34055)].
scientific article; zbMATH DE number 2117916