Robust impulse nonlinear delayed multi-agent systems: an exponential synchronization

This work explores the use of state-feedback pinning control in the presence of time-varying delay to solve the synchronization problem of uncertain nonlinear multi-agent systems (MASs). To begin, it is assumed that the agent's communication topology is a directed, static network. Second, the synchronization issue is transformed into the typical closed-loop system stability issue by employing Laplacian matrix inequality (LMI). The primary goal of this study is to construct a state-feedback pinning controller that yields a closed-loop system that is stable under all permissible uncertainty and impulsive cases. To achieve this goal, we develop a new set of delay-dependent synchronization criteria for the closed-loop system by constructing an appropriate Lyapunov functional and making use of Kronecker product features in conjunction with matrix inequality approaches. All that's needed to construct the optimal state-feedback controller is a set of constraints in the form of linear matrix inequalities, which can be solved with any number of powerful optimization methods. To further illustrate the practicality and efficiency of the suggested control design system, a numerical example and associated simulations are provided.