Periodic and dynamic periodic event-triggered control for nonlinear cyber-physical systems under DoS attacks via a hybrid system approach

This paper is focused on the problem of periodic and dynamic periodic event-triggered control for nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks and exogenous disturbances. The analysis relies on a new model to design periodic event-triggered control and dynamic periodic event-triggered control schemes such that the nonlinear CPSs are resilient to a class of malicious attacks which can be characterized by attacking frequency and attacking duration. By developing an average dwell-time automaton and a time-ratio monitor to describe frequency and duration of the DoS attacks, general hybrid dynamical frameworks are firstly proposed for event-triggered nonlinear CPSs. Based on the established models, novel Lyapunov functions are constructed. Furthermore, thanks to the Lyapunov-based approach, $L_{2}$ -gain performance of the considered nonlinear CPSs under DoS attacks is analyzed. Finally, the feasibility of the theoretical findings is demonstrated by a numerical example.