Semiglobal synchronization of multiple generic linear agents with input saturation

This paper investigates the semiglobal synchronization problem for a group of agents with input saturation under directed interaction topology, where each agent is modeled as a generic linear system rather than the single-integrator or double-integrator dynamics. The main result is the construction of a feedback coupling gain that achieves semiglobal synchronization if all the agents have identically saturated linear dynamics, which can be of any order. It is shown that the coupling gain obtained via parametric Lyapunov equations can semiglobally synchronize any directed network provided that the interaction topology has a directed spanning tree. Furthermore, due to the use of parametric Lyapunov equations, a convergence rate is analytically obtained. Finally, a simulation example is provided to demonstrate the effectiveness and advantages of our theoretical findings.