Guaranteed performance impulsive tracking control of multi-agents systems under discrete-time deception attacks

This paper is concerned with the impulsive consensus tracking problem of Lipschitz nonlinear multi-agent systems subject to deception attacks. The proposed distributed impulsive tracking algorithm allows only partial state variables of every agent to be governed by consensus impulses. The considered deception attacks are supposed to take place in the controller–actuator channel, and can be modelled by a set of Bernoulli processes. By considering the discrete-time deception signal as bounded external disturbance, the consensus tracking problem reduces to the exponential input-to-state stable (EISS) problem of the tracking error system. The EISS-gain is used as an assessment index in measuring the capacity of consensus control laws for attenuating attacks. Specifically, a novel EISS analysis method combined with the use of a weighted discontinuous Lyapunov function is proposed to establish the consensus tracking criterion. A convex optimization problem with linear matrix inequalities-based constraints is formulated to design the guaranteed performance distributed impulsive controller, which makes the EISS-gain as small as possible. Two illustrated examples quantify the effectiveness of the proposed analysis and design approach.