Stabilization of Periodic Piecewise Time-Varying Systems With Time-Varying Delay Under Multiple Cyber Attacks: An Augmented Lyapunov Functional Approach

This article investigates the asymptotic stabilization of periodic piecewise time-varying systems with time-varying delay under various cyber attacks, particularly deception and DoS attacks. The addressed system is reformed into a number of time-varying subsystems based on the time interval for each period. Following that, a state-feedback controller with periodic time-varying gain parameters is developed to solve the stabilization problem. The control design depicts the possibility of the aforementioned cyber attacks with two mutually exclusive stochastic Bernoulli distributed parameters. Then, an augmented Lyapunov-Krasovskii functional with periodically varying matrices is used to determine the conditions for designing the proposed controller that ensures the mean-square asymptotic stability of the addressed system. The results of numerical examples support the conclusion that the proposed method is effective and superior, regardless of the cyber attacks involved.