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There exist bounded transmission delay and data packet dropout in the networked control systems (NCSs). When the sensors and actuators are time-driven and controllers are event-driven, the NCSs can be modelled as a class of discrete-time systems with time-varying input delay. Most of similar articles simply combine delay and packet dropout to analyse and synthesise NCSs without distinguishing their different impacts, which leads to conservative results. In this study, the authors summarise that the number of consecutive data packet dropout increases gradually in case of packet dropout. A novel Lyapunov-Krasovskii functional is constructed based on this increment property, so less conservative results are obtained through the Lyapunov-Krasovskii functional approach. In addition, the upper bound of a Lyapunov functional difference cross term is reasonably estimated to further reduce the conservativeness. Stability and stabilisation criteria which are separately related to the transmission delay and data packet dropout are presented. The obtained conditions are based on linear matrix inequalities, which can be solved easily by MATLAB or other numerical software.

a b s t r a c tThis paper introduces a model based upon games on an evolving network, and develops three clustering algorithms according to it. In the clustering algorithms, data points for clustering are regarded as players who can make decisions in games. On the network describing relationships among data points, an edgeremoving-and-rewiring (ERR) function is employed to explore in a neighborhood of a data point, which removes edges connecting to neighbors with small payoffs, and creates new edges to neighbors with larger payoffs. As such, the connections among data points vary over time. During the evolution of network, some strategies are spread in the network. As a consequence, clusters are formed automatically, in which data points with the same evolutionarily stable strategy are collected as a cluster, so the number of evolutionarily stable strategies indicates the number of clusters. Moreover, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the comparison with other algorithms also provides an indication of the effectiveness of the proposed algorithms.

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each player's expected payoff is calculated. Later, he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.