A chattering free consensus controller for multiple Lur'e systems with a non-autonomous leader and directed switching topology

Achieving asymptotical cooperative goal for multi-agent systems (MASs) with non-autonomous leaders (i.e., leaders with nonzero inputs) is a critical but challenging issue. Traditional approach is to use discontinuous controllers which may cause chattering phenomenon in practical applications. How to achieve the asymptotical goal via a chattering free cooperative controller remains to be open so far. In this paper, an adaptive continuous controller is designed to achieve zero error consensus tracking in multiple Lur'e systems with a non-autonomous leader under directed switching topology. Firstly, an unknown input observer (UIO) based on relative outputs is given to estimate the relative full states. Then an adaptive continuous controller is designed by introducing a decay function which remains positive into the term that plays the role of eliminating the impacts of leader's nonzero inputs. Secondly, by using multiple Lyapunov functions (MLFs) technique, it is proven that zero error consensus tracking can be achieved if the average dwell time (ADT) is greater than a positive threshold. Finally, theoretical result is verified by performing simulations on Chua's circuits. Compared with existing work, the proposed controller can not only achieve asymptotical consensus, but also is chattering free.