Abstract
In this paper, we investigate sampled-data stabilization of memristor nonlinearity in Chua's circuits. The system stability pertaining to its switching nonlinearity covers two situations of flux thresholds. Through the stability analysis, the multistability characteristic is proved by its periodic invariant stable line. Moreover, the dynamical features of the considered system are examined in details by numerical and corresponding simulated experiments. Several statistical and analytical characteristic methods are used to confirm the existence of chaotic attractors. With the help of Lyapunov stability theory, new sufficient conditions are formulated using the linear matrix inequality (LMI) method to ensure robust stability and stabilization of closed-loop systems. Finally, we present a numerical example to ascertain the validity of the theoretical results obtained.
Highlights
A memristor, i.e., a fourth-order basic passive circuit, was theoretically discovered by Chua in 1972 [1], while its existence was experimentally proved in 2008 [2]
The general working principles of a memristor component are like a simple switch where it switches from a low resistive state to a high resistive state and vice versa
To the best of the authors’ knowledge, the existing published literature does not provide the results of sampled-data stabilization of LPV memristor-based Chua’s circuits (MCCs), and this is the motivation of this article
Summary
A memristor, i.e., a fourth-order basic passive circuit, was theoretically discovered by Chua in 1972 [1], while its existence was experimentally proved in 2008 [2]. To the best of the authors’ knowledge, the existing published literature does not provide the results of sampled-data stabilization of LPV memristor-based Chua’s circuits (MCCs), and this is the motivation of this article. In this manuscript, the considered system has peculiar and very interesting nonlinear characteristics nature i.e., non smooth boundary switching type [45], [46].
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