On Consensus of Second-Order Multiagent Systems With Actuator Saturations: A Generalized-Nyquist-Criterion-Based Approach

In this article, a frequency-domain approach is developed to deal with the global consensus problem for a class of general second-order multiagent systems (MASs) subject to actuator saturations. By employing the describing function and the generalized Nyquist criterion, the global consensus problem is thoroughly investigated for both undirected and directed topologies. First, the describing function is introduced to characterize the actuator saturations in the s -plane, and the inherent representation error is quantitatively analyzed from a frequency-domain perspective. Then, by means of the Kronecker product, the addressed consensus problem of the MAS is transformed into a corresponding stability analysis problem for a certain multi-input-multi-output (MIMO) system and, consequently, the generalized Nyquist criterion for MIMO systems is exploited to derive the condition for the global consensus of the MAS where the impact from the actuator saturation is explicitly reflected. Finally, numerical simulations are provided to illustrate the validity of the proposed theoretical result.