Establishing the graph-based criterion for the selection of any location and any number of leaders is the main difficulty in the complete graphic characterization of multiagent controllability. This greatly increases the complexity of the study, compared with the results derived for only one or several classes of leaders. Through a detailed analysis of graphs of six nodes, this article presents a systematic design and identification process for the complete graphic characterization by taking advantage of controllability destructive nodes. The topologies obtained by the proposed method allow directly determining controllability at the network topology level. The results are not only applicable to any leader's selection but also reveal the difficulty and complexity in the study of complete controllability graphic characterizations. Moreover, by comparing graphs composed of five and six nodes, the results reveal the graph-theory-based controllability complexity caused by adding only one node. Finally, results are derived to show how to design topology structures to ensure the controllability under any selection of leaders.

This paper mainly focuses on the optimal output feedback control and stabilization problems for discrete-time multiplicative noise system with intermittent observations. The main contributions of this paper can be concluded as follows. First, different from the previous literatures, this paper overcomes the barrier of the celebrated separation principle for stochastic control problems of multiplicative noise systems. Based on the measurement process, the optimal estimation is presented, and by using dynamic programming principle, the optimal output feedback controller is designed with feedback gain based on the given coupled Riccati equations. Second, the necessary and sufficient stabilization conditions for multiplicative noise system with intermittent observation in the mean square sense are developed for the first time. Finally, the novel results developed in this paper can be applied to solve the output feedback control and stabilization problems for general networked control system of user datagram protocol network case. The range of packet losses rate and the allowable maximum packet losses rate are presented explicitly.

This paper mainly considers the optimal measurement feedback control and stabilization for networked control systems (NCSs) with packet losses. The problems are involved with fundamental difficulties of separation principle and optimal estimation (conditional expectation) for multiplicative noise stochastic systems. First, the optimal estimator (conditional expectation) for NCSs with packet losses is derived and the optimal measurement feedback controller is obtained by using the maximum principle. The sufficient and necessary solvability condition of finite horizon measurement feedback control problem is first presented. Moreover, the asymptotic stability of the optimal estimator is studied. Finally, for the infinite horizon case, based on the introduction of a new Lyapunov function, which is defined with the optimal cost function, it is shown that the system is stabilizable in the mean square sense if and only if an algebraic Riccati equation admits a unique positive definite solution.