Executive Summary : | The main aim of this study is to investigate the finite and fixed time stability and stabilization of a class of nonlinear systems with delayed impulsive effects. In this study, two main impulsive systems will be investigated, such as systems with time-dependent delayed impulses and systems with state-dependent delayed impulses. In the first phase, the finite/fixed-time stability and stabilization conditions will be derived based on Lyapunov-functional, the Razumikhin technique, and the linear matrix inequality approach for impulsive nonlinear systems. In the second phase, the effect of delayed impulses will be implemented in recent control schemes, for example, event-trigged control and sampled control schemes. Based on the new control scheme, researchers will analyze the stabilization and synchronization problems in complex dynamical networks, impulsive consensus control problems, and multi-agent systems. Then corresponding finite and fixed time stabilization and synchronization criteria will be derived on the basis of the Lyapunov-functionals with impulsive phenomena and LMI approaches. The derived conditions will be validated with impulsive dynamical systems and their numerical parameters. From the simulation results, the superiority of the control scheme and the derived conditions will be confirmed with existing approaches. This approach will provide a new theoretical framework for impulsive control systems in applications of micro-grid power systems and energy networks. |