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In this paper, adaptive observers are designed for a class of Lipschitz nonlinear systems. These observers are featured with the property of finite-time convergence of state estimation and unknown parameter estimation under some normal persistence excitation condition. The convergence are obtained by assuming existence of a Lyapunnov function under certain condition, by the finite-time stability and...
In this paper, a global finite-time observer is designed for a class of nonlinear systems with non-Lipschitz conditions. Compared with the previous results, the observer designed in this paper is proposed with a new gain update law. By two examples, we show that the proposed observer can reduce the time of the observation error convergence.
In literature it is conjectured that the states of the generalized Lorenz system with an unknown parameter can not be estimated by adaptive observers. In this paper we show that this unknown parameter and the states can actually be estimated simultaneously by some kind of adaptive observer. The proof is obtained by constructing some exponential observer to achieve chaotic synchronization for the generalized...
In this article, we achieve chaotic synchronization in a new chaotic system suggested in [1], which cannot be estimated by some kind of adaptive observers without knowing the exact system parameters. Unlike the reference [1], we use the adaptive observer introduced in [2]. We also give conclusive proof that the output of the chaotic system satisfies the persistently exciting (PE) condition.
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