Noise tolerance leader-following of high-order nonlinear dynamical multi-agent systems with switching topology and communication delay

This paper investigates the leader-following tracking consensus problem for high-order nonlinear dynamical multi-agent systems with switching topology and communication delay under noisy environments. In order to reflect a more realistic situation, we introduce a general multi-agent systems model and also further investigate its robust consensus under noisy environments, the topology of the network is assumed to be in a finite set of arbitrarily stochastic switching, the communication delay is also considered in the tracking control protocols. The mean square consensus sufficient conditions of multi-agent systems are explored via the common stochastic Lyapunov functional stability theory, in other words, can be solved by linear matrix inequality schemes. The mean square consensus condition is derived to provide a rigorous condition for leader-following of high-order nonlinear dynamical multi-agent systems with considerable scale. In particular, we prove that the proposed algorithm is robust against the bounded communication delay in noisy environments. On the other hand, when it involves many multi-agent systems, a more conservative but effective consensus protocol is also raised. The consensus protocols only require low-dimensional matrices, which are independent of the network size. In addition, the consensus criteria of two cases without communication delay or noisy environment are also proposed. A simple optimization program is also developed to determine the maximum allowable communication delay. Finally, in order to demonstrate the effectiveness and feasibility of the consensus protocol obtained in this paper, the numerical examples are given.