Predefined-sequential-synchronized control with exploration of event-triggered mechanism

This paper investigates the (strict-) predefined-sequential-synchronized control problem, i.e., the state components of the system can reach the equilibrium in a predefined convergence sequence within a predefined time interval. Both the predefined convergence sequence and the predefined convergence time can be customized arbitrarily. This approach develops properties called (sampled) weighted ratio persistence, which characterize the relationship between the dynamics and the states of the system. Lyapunov-type theorems are established to provide sufficient conditions for (strict-) predefined-sequential-synchronized stability. Controller designs for first- and second-order systems are presented as illustrative examples to establish the overall controller design framework. Furthermore, the integration of event-triggered mechanisms is explored to alleviate communication loads while preserving control performance. Simulation is showcased to highlight the effectiveness of the designed controllers.