Event-Triggered Impulsive Control for Switched Systems Under Aperiodic Denial-of-Service Attacks

Source abstract

Ensuring input-to-state stability (ISS) of networked control systems under simultaneous mode switching and cyber attacks is a challenging open problem, since the asynchronous interplay among continuous dynamics, event-triggered impulses, and aperiodic denial-of-service (DoS) blockages has not been addressed in a unified nonlinear framework. This paper establishes such a framework by integrating a mode-dependent event-triggered mechanism (MDETM) with the admissible edge-dependent average dwell time (AED-ADT) approach for continuous-time nonlinear impulsive switched systems. Under mild Lyapunov-based conditions, rigorous sufficient conditions are derived that (i) guarantee a strictly positive uniform inter-event lower bound Δ̲>0, and (ii) establish global ISS with an explicit exponential decay rate η>0 that quantifies the trade-offs among the AED-ADT limit, the DoS frequency/duration parameters (τD,τd), and the triggering coefficients (ak,dk). The nonlinear framework is further specialized to linear systems, yielding tractable Linear Matrix Inequality (LMI) criteria. Numerical validation on a two-subsystem linear impulsive switched system confirms the theoretical predictions: the LMI solver returns η=0.451, a Zeno-free lower bound Δ1=0.0103 s, and the state converges from x(t0)=[100,−100]⊤ to ∥x(10)∥=0.0011 under an average DoS duty cycle of approximately 15%.