This paper models a class of leader-based discrete-time multi-agent systems (MASs) over signed networks with both positive edges and negative edges, and addresses the observability of such multi-agent network based on an agreement protocol. Some new algebraic and graphical characterisations of observability are given using a signed Laplacian. In addition, for a structurally balanced network, all the followers can be observable if the leaders are selected from the same partitioned subset, namely, the observability of a leader-follower discrete-time signed network with structurally balanced condition is equivalent to that of the corresponding unsigned network. Some numerical examples and simulations are given to demonstrate the analysis.

This paper proposes a new second-order discrete-time multiagent model and addresses the controllability of second-order multiagent system with multiple leaders and general dynamics. The leaders play an important role in governing the other member agents to achieve any desired configuration. Some sufficient and necessary conditions are given for the controllability of the second-order multiagent system. Moreover, the speed controllability of the second-order multiagent system with general dynamics is discussed. Particularly, it is shown that the controllability of the whole system relies on the number of leaders and the connectivity between the leaders and the members. Numerical examples illustrate the theoretical results.

This paper is concerned with the problems of absolute stability and master-slave synchronization of systems with state-dependent nonlinearities. The Kalman-Yakubovich-Popov (KYP) lemma and the Schur complement formula are applied to get novel and less conservative stability conditions. A numerical example is presented to illustrate the efficiency of the stability criteria. Furthermore, a synchronization criterion is developed based on the proposed stability results.