Low‐chattering consensus of second‐order multi‐agent system based on implicit discrete‐sliding mode control

Abstract This paper addresses the distributed leader‐following consensus control problem for discrete‐time second‐order multi‐agent systems. A novel implicit discrete‐sliding mode controller is introduced, offering the key advantage of mitigating the chattering phenomenon typically associated with the traditional explicit discrete‐time sliding mode control method. It is shown that with proper controller parameters, the sliding surface can be reached in finite steps. Then the consensus errors will converge to zero exponentially. A mixed linear complementarity problem (MLCP) is established to solve for the implicit discrete‐sliding mode control input. Details about the implementation are presented, such as the information that is needed to obtain the solution of the MLCP. Finally, numerical examples are given to demonstrate the theoretical results.