H∞ synchronization of coupled delay partial differential systems via nonsingular transformation method

This paper considers the H∞ synchronization of coupled delay partial differential systems (PDSs). By using the nonsingular transformation method, the coupled systems are decoupled to simplify the complex H∞ synchronization problem of coupled delay PDSs. The equivalence of the H∞ synchronization for original coupled delay PDSs and the H∞ stabilization of transformed decoupled delay PDSs is rigorously verified. Sufficient conditions are obtained to guarantee the H∞ synchronization. These sufficient conditions also reflect the effect of spatial domain on the H∞ synchronization. Moreover, when the external disturbances disappear, the asymptotical synchronization is studied. The relationship between the H∞ synchronization and the asymptotical synchronization is also presented. At last, an example is given to illustrate the correctness of our results.