Robust H_∞ Synchronization of Coupled Partial Differential Systems With Spatial Coupling Delay

Abstract

This brief discusses the asymptotical synchronization and robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization for coupled semilinear partial differential systems (PDSs) with time-varying delay in spatial coupling. First, using the Lyapunov-Krasoviskii functional method, sufficient conditions are obtained for the asymptotical synchronization of coupled semi-linear time-delay PDSs and these conditions are presented by linear matrix inequalities (LMIs), which are easy to be solved. The effect of the spatial domain on the asymptotical synchronization of the coupled time-delay PDSs is also presented. Then the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization is considered in temporal-spatial domain for the coupled time-delay PDSs with external disturbances. In terms of the technique of completing squares, sufficient conditions are got for the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization of time-delay coupled PDSs. Finally, numerical examples of coupled semilinear time-delay PDSs are given to illustrate the correctness of the obtained results.