Local exponential stabilization of delayed nonlinear systems via event‐triggered control

The linearization method is a fundamental tool for applying linear system theory to nonlinear systems and requires the vector field of the studied system to be differentiable. This paper investigates the local stabilization problem of discrete‐time nonlinear systems with time‐varying delays under event‐triggered control, using the linearization method. Note that even if a system itself is differentiable, the closed‐loop system is generally discontinuous due to the state jumps caused by event‐triggering. The basic idea of this paper is to design an event‐triggered state‐feedback controller for the linearized system, thereby achieving ultimate stabilization of the original nonlinear system. For this purpose, the system is transformed into an equivalent delay‐free switched system via the switching transformation method. Several sufficient conditions for local exponential stabilization of the original system are derived by constructing a quadratic switched Lyapunov function based on the equivalent switched system, and two kinds of delays are considered: Arbitrarily and slowly time‐varying ones. It is, to the best of our knowledge, the first time that the linearization method has been applied to event‐triggered control. A numerical example is provided to verify the effectiveness of the results proposed.