Monotone decreasing LKF method for synchronization of heterogeneous nonlinear switched time-delay multi-agent systems with an uncertain target

This paper investigates the synchronization problem of heterogeneous nonlinear switched time-delay multi-agent systems (MASs) with an uncertain target. Due to the heterogeneous, nonlinear, and switching features, considering different time-delays among agents and unknown inputs on the target poses a huge challenge in achieving synchronization. To solve this challenging issue, a new protocol that incorporates distributed observers, distributed controllers, and a time-varying positive-definite matrix function is designed to estimate the states of the target and compensate for errors among agents. Moreover, by proposing a novel Lyapunov–Krasovskii functional (LKF), this paper not only obtains synchronization criteria but also has an interesting characteristic: the LKF is monotonically decreasing at any time, even at any switching instants. Finally, as some applications, heterogeneous switched Chua’s circuits and flexible-joint robots are given to demonstrate the effectiveness of the proposed new protocol and LKF.