On Novel Design Methods of Fixed-Time State Observation and Consensus Control for Linear Leader–Follower Multiagent System

In this paper, the fixed-time consensus problem for leader–follower multiagent systems with directed graphs is discussed. First, a new fixed-time state observer of the multiagent system is designed. In the new state observer, an auxiliary matrix is introduced which can be theoretically obtained by solving a linear matrix inequality. The important role of the auxiliary matrix is that it makes the upper bound of the fixed time for the state observation of multiagent system solvable and more accurate, which enable the observation error system converges faster. Based on the new fixed-time state observer, a sufficient condition is given with which the observation of the state of multiagent system can be reached in fixed time. Second, a new fixed-time control protocol is designed for the leader–follower multiagent system. In the new controller, another auxiliary matrix is introduced which can also be theoretically obtained with linear matrix inequality. With the new control protocol, the closed-loop leader–follower multiagent system is theoretically shown that the fixed-time consensus can be reached in fixed time by means of the concept of fixed-time stability, Lyapunov stability theory, and LaSalle’s invariance principle. The important role of the new control protocol is that it also makes the fixed time for the consensus multiagent system solvable and then the closed-loop multiagent system converges faster. Finally, some numerical simulations are presented to demonstrate convincingly the superiority of the method and results obtained in this paper. From the simulations, it can be seen that in comparison with some existing works, the estimate of fixed time for the consensus problem may be more accurate and faster.