Abstract
This paper discusses the asymptotical synchronization and H∞ synchronization of coupled neutral-type delay partial differential systems (NDPDSs). A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. By using the method of a nonsingular matrix transformation, we decouple the coupled error dynamical systems. Then, sufficient conditions that guarantee the asymptotic stability of decoupled synchronization error dynamical systems are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and by using Jensen׳s inequality and reciprocally convex combination technique, which implies the asymptotical synchronization of the coupled NDPDSs. Moreover, the stability criteria for the H∞ stabilization of decoupled synchronization error dynamical systems with external disturbances are also derived in terms of LMIs, which guarantee the H∞ synchronization of the coupled NDPDSs. The equivalence between the H∞ stability of decoupled synchronization error dynamical systems and the H∞ synchronization of coupled NDPDSs is also proved by mathematical analysis. Finally, numerical examples are provided to demonstrate the effectiveness of the obtained results.
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