A synchronizing second order sliding mode control applied to decentralized time delayed multi−agent robotic systems: Stability Proof

This study investigates the synchronization issue of multiple robot manipulators in the presence of time delay. Since several previous works based on synchronization task neglect the communication delay, in this paper we develop a finite time stability based on a Lyaponov functional for synchronization of a networked robotic system where time delay exists during the communication between robots. To this effect, we consider a second order sliding mode control (SMC) combined with the cross coupling concept in order to ensure the position synchronization of networked robot manipulators. Furthermore, the stability of the proposed controller with communication’s delay has been proved. Simulation results illustrate satisfactory performances which prove the efficiency of the proposed approach