Global pulse synchronization of chaotic oscillators through fast-switching: theory and experiments

Experiments on node-to-node pinning control of Chua’s circuits

“…Similarly to the case of master-slave synchronization problems, see for example [26][27][28][29], pinning controllability problems can be generally cast into classical stability problems for nonlinear systems. More specifically, network synchronization can be described by the error dynamics, that represents the difference between the states of the network oscillators and the state of the reference oscillator.…”

Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators

“…We note that, in consensus theory, the individual oscillators' dynamics is linear while in the present case the coupled systems are strongly nonlinear. We further observe that results in [26,[40][41][42][43][44][45][46][47][48] are only for analog dynamical systems. In this paper, the inherent nonlinear nature of the coupled systems is retained, the problem is cast into a sampled-data setting, global synchronization properties are explored, and experiments are used for validation.…”

“…The type of intermittent coupling considered in this paper has been analyzed in the framework of consensus theory for continuous-time systems [38,39] and synchronization of analog complex networks [26,[40][41][42][43][44][45][46][47][48]. We note that, in consensus theory, the individual oscillators' dynamics is linear while in the present case the coupled systems are strongly nonlinear.…”

An overview on averaging for pulse-modulated switched systems

“…In the case of T -periodic switching function in [6] the local stability of the switched system (3) based on that of the time-invariant averaged system (9) is proved, and in [7], [13] the extension to global stability is shown. Moreover in the general case of non-periodic switching functions in [21] it is shown how the stability of the time-invariant averaged system (9) can infer some practical stability results on the switched system (3).…”

“…Averaging is a widely used technique in the power electronics community since 1970's [3], [4]. The averaging approach has been also applied to other switched systems of practical interest such as multi-agent systems [5], synchronization of oscillators [6], [7], pneumatic systems [8], switched controllers [9], [10], congestion control mechanism [11], robotic manipulators [12], and nonlinear circuits [13].…”