Decentralized Control of Large-Scale Systems Under Asynchronous Denial-of-Service

Abstract

This paper considers large-scale networked control systems with network communications undergoing denial-of-service (DoS) attacks. The local networks operate asynchronously and independently of each other in the presence of sampling instants and DoS attacks. We assume that the actuators refuse to work during DoS attack intervals. We design a piece-wise continuously differentiable auxiliary timer for each subsystem and use the graph-theoretic technique to deal with the crossing terms. Based on the auxiliary timer, we introduce a discontinuous Lyapunov functional (which is a mixture of vertex-Lyapunov functionals and vertex-Lyapunov functions) that does not grow at DoS on/off transitions. We obtain linear matrix inequality (LMI) conditions for finding the maximal allowable DoS duration that preserves stability. Finally, an example of coupled two inverted pendulums demonstrates our results and shows that the discontinuous Lyapunov functional improves the results compared with the continuous common one.