Almost Sure Stability of Nonlinear Systems Under Random and Impulsive Sequential Attacks

This article is concerned with the stability problem for a class of Lipschitz-type nonlinear systems in networked environments, which are suffered from random and impulsive deception attacks. The attack is modeled as a randomly destabilizing impulsive sequence, whose impulsive instants and impulsive gains are both random with only the expectations available. Almost sure stability is ensured based on Doob's Martingale Convergence Theorem. Sufficient conditions are derived for the solution of the nonlinear system to be almost surely stable. An example is given to verify the effectiveness of the theoretical results. It is shown that the random attack will be able to destroy the stability, therefore, a large feedback gain may be necessary.