Chaos synchronization based on unknown input proportional multiple-integral fuzzy observer.(English)Zbl 1421.93082

Summary: This paper presents an unknown input proportional multiple-integral observer (PIO) for synchronization of chaotic systems based on Takagi-Sugeno (TS) fuzzy chaotic models subject to unmeasurable decision variables and unknown input. In a secure communication configuration, this unknown input is regarded as a message encoded in the chaotic system and recovered by the proposed PIO. Both states and outputs of the fuzzy chaotic models are subject to polynomial unknown input with $$k$$th derivative zero. Using Lyapunov stability theory, sufficient design conditions for synchronization are proposed. The PIO gains matrices are obtained by resolving linear matrix inequalities (LMIs) constraints. Simulation results show through two TS fuzzy chaotic models the validity of the proposed method.

MSC:

 93C42 Fuzzy control/observation systems 34H10 Chaos control for problems involving ordinary differential equations 34D06 Synchronization of solutions to ordinary differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C15 Control/observation systems governed by ordinary differential equations
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