Finite/fixed-time bipartite consensus for networks of diffusion PDEs via event-triggered control

Abstract

This paper investigates the finite/ fixed-time bipartite consensus for networks of diffusion partial differential equations (PDEs) via the event-triggered control strategy. A global convergence principle in fixed time, which plays an important role in the theoretical analysis later, is developed for nonlinear systems. The C0-semigroup method is adopted to explain the well-posedness of the considered network systems. Two new event-triggered control protocols are designed to realize the finite/ fixed-time bipartite consensus goal. By applying the proposed convergence principle, Lyapunov functional approach and inequality analysis technique, the finite/ fixed-time bipartite consensus conditions are addressed under the designed control mechanism. Moreover, the settling time is estimated accurately. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.