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

Authors
Journal
Communications in Nonlinear Science and Numerical Simulation
1007-5704
Publisher
Elsevier
Publication Date
Volume
15
Issue
12
Identifiers
DOI: 10.1016/j.cnsns.2010.01.035
Keywords
  • Sampled-Data
  • Chaos
  • Synchronization
  • Linear Matrix Inequality
  • Microcontroller
Disciplines
  • Communication

Abstract

Abstract In this paper, we consider the problem of synchronizing a master–slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master–slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master–slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master–slave chaotic system based on Chua’s circuit.

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