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

Abstract

a b s t r a c tThis paper considers the H 1 synchronization of coupled delay partial differential systems (PDSs). By using the nonsingular transformation method, the coupled systems are decoupled to simplify the complex H 1 synchronization problem of coupled delay PDSs. The equivalence of the H 1 synchronization for original coupled delay PDSs and the H 1 stabilization of transformed decoupled delay PDSs is rigorously verified. Sufficient conditions are obtained to guarantee the H 1 synchronization. These sufficient conditions also reflect the effect of spatial domain on the H 1 synchronization. Moreover, when the external disturbances disappear, the asymptotical synchronization is studied. The relationship between the H 1 synchronization and the asymptotical synchronization is also presented. At last, an example is given to illustrate the correctness of our results.

Finite‐time synchronization of a class of N‐coupled complex partial differential systems with time‐varying delay

“…Research on partial differential systems (PDSs) have elicited considerable attention recently . In practice, numerous phenomena, such as those in chemical engineering, neurophysiology, and biolynamics, occur.…”