Event-Triggered Control of a Class of Nonlinear Systems on the Basis of Indefinite Lyapunov Theory

This brief proposes event-triggered rules for stabilizing the equilibrium point of a class of nonlinear systems, on the basis of indefinite Lyapunov theory. Unlike the traditional event-triggered control methods, which have been constructed based on the Lyapunov theory, the time-derivative of the corresponding Lyapunov function can be positive in some time periods by using the proposed event-triggered rules. For a class of uncertain nonlinear systems with matched uncertainty, the proposed event-triggered controller guarantees that the trajectories of the system tend to an arbitrary small neighborhood of the equilibrium point of the system. Numerical examples confirm the obtained analytical results.