Master-slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators. (English) Zbl 1222.93148
Summary: 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.
MSC:
| 93C57 | Sampled-data control/observation systems |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37N35 | Dynamical systems in control |
| 93D15 | Stabilization of systems by feedback |
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