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This article investigates the problems of structural balance and distributed control for a high-order signed network with generic linear dynamics. A novel approach is proposed to analyze the structural balance of a general network based on the strongly connected components of the topology graph and the Frobenius normal form of the adjacency matrix. To address the distributed control of high-order signed networks, both state-feedback and observer-type algorithms are developed on the basis of low-gain strategies, where a unified framework is presented to construct full- or reduced-order observers. The dynamical behaviors of the signed network under the proposed algorithms are systematically explored, where the nontrivial final network state is computed by employing an eigenvector-based approach. The theoretical results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we study the finite-time stabilization and the asymptotic stabilization with probability one of Markovian jump Boolean control networks (MJBCNs) by sampled-data state feedback controls (SDSFCs). Based on the semi-tensor product (STP), we introduce an augmented variable multiplied by the vector form of the switching signal and the state of MJBCN. We find that under SDSFC, the sequence of the states of the augmented variable at sampling instants satisfies the Markov property. Based on the convergences of the switching signal and the augmented variable, we obtain the sufficient and necessary criteria for the finite-time stabilization and the asymptotic stabilization of MJBCNs by SDSFCs, respectively. Moreover, for the two kinds of stabilization, the feedback matrices of SDSFCs are constructed, respectively. Finally, the obtained results are applied to an apoptosis network and a model of the lactose operon in the Escherichia Coli. [ABSTRACT FROM AUTHOR]

A new type of asymptotic stability for nonlinear hybrid neutral stochastic systems with constant delays was investigated recently, where the criteria depended on the delays’ sizes. Unfortunately, developed theory so far is not sufficient to deal with challenging problems of the decay rate, time-varying delays, and nonautonomous issues. These problems have not been tackled in the existing literature. Consequently, under the weak constraints, this article focuses on the general decay, including the exponential stability and the polynomial stability, for nonlinear nonautonomous hybrid neutral stochastic systems with time-varying delays by the approach of the multiple degenerate functionals. Moreover, this article derives the interesting assertions related to the general $H_{\infty }$ stability and the polynomial growth at most. [ABSTRACT FROM AUTHOR]

This paper investigates a distributed static and dynamic self-triggered impulsive control for nonlinear multiagent systems (MASs) where the impulsive gains follow a normal distribution, respectively. By integrating the distributed self-triggered control scheme with the impulsive control approach, a novel distributed impulsive controller is developed. The goal of the consensus of MASs can be realized using the proposed methods and several consensus criteria are obtained. Our schemes have some distinct superiorities, including the impulsive gains obeying a normal distribution, avoiding the continuous communication, and reducing the sampling frequency. Hence, compared with the existing literature, the conservativeness coming from the limitation of impulse gain and the sampling frequency is degraded, and it effectively extends the generality of the method in the practical application. Finally, the effectiveness of the theoretical results is demonstrated by two simulations. [ABSTRACT FROM AUTHOR]

This article investigates the reliable output feedback control problem for networked nonlinear semi-Markov jump systems, in which a control strategy with redundant channels is established to reduce the adverse effect caused by packet dropouts. The actuator faults are fully considered in the setup. On the basis of stochastic analysis theory and fuzzy-model-based method, some criteria are established to guarantee the $\sigma $ -error mean-square stability for the considered systems. As a consequence, the reliable output feedback controller design method is proposed, which can be utilized to deal with the actuator failures problem effectively. Finally, two illustrative examples are employed to explain the availability of the presented design approach, where the single-link robot arm system model is contained. [ABSTRACT FROM AUTHOR]

We propose Lyapunov functions for the set stability of Boolean networks (BNs) and control Lyapunov functions for the feedback set stabilization and the synchronization of Boolean control networks (BCNs) in this brief. Meanwhile, some propositions of these Lyapunov functions are put forward. Sufficient and necessary conditions for the set stability of BNs, the feedback set stabilization of BCNs and the synchronization of drive-response coupled BCNs in the form of Lyapunov functions are presented successively. Moreover, an algorithm is given to construct control Lyapunov functions and state feedback controllers simultaneously for the synchronization of coupled BCNs. Two examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, a continuous-time multiagent system is proposed for solving optimal resource allocation problems with local allocation feasible constraints. In the system, all the primal agents are divided into different groups. We use dual variables which describe the dual agents to represent the groups of the original agents. The groups of dual agents are used to communicate with others on behalf of the primal agents to reduce communication costs. That is to say, primal agents aim to seek their own optimal solutions by using local information. And dual agents represent primal agents to communicate with other agents in different groups by using the whole group information. The two kinds of agents cooperate to find the optimal solution of the problem. In this way, we only need to know the connections of dual agents to design the multiagent network, and do not need to consider the connections of the primal agents. So the communication cost and the amount of variables will be largely reduced especially for large-scale problem. Furthermore, it is proved that the multiagent system can reach consensus with respect to the dual variables. At the same time, the primal variables are convergent to the optimal solutions of the optimization problem under some certain assumptions on the communication network. For large-scale problem if we take the groups as areas, then the system is suitable for multiarea problem. Simulation results are presented to demonstrate the performance of the proposed multiagent system. [ABSTRACT FROM AUTHOR]

Event-triggering strategy is a control implementation technique which intends to minimizing resource usage while achieving the acceptable performance of the closed-loop system. In this paper, an event-triggered sliding mode control (SMC) is designed for attitude stabilization of a rigid spacecraft subject to external disturbances and model uncertainties. A semi-global event-triggering strategy is proposed for SMC to keep the system trajectory in the vicinity of a proposed sliding surface. Since in this sliding surface, the sliding mode is asymptotic stable, the trajectories of the attitude control system remain ultimately bounded under the circumstance of disturbances and uncertainties. Moreover, the given event-triggered control implementation is only dependent on the angular velocity at sampling instant and triggering strategy with Zeno phenomenon can be avoided. Some numerical simulations are shown to illustrate the availability of the obtained results. [ABSTRACT FROM AUTHOR]

This brief investigates the set stabilization of Boolean control networks (BCNs) with impulsive effects via event-triggered control (ETC) scheme. An algorithm is designed to find the largest control invariant set, then its efficiency is authenticated. An interesting phenomenon is that some states may leave from the control invariant set at impulsive time steps. Afterward, a necessary and sufficient criterion is derived to determine the set stabilization of event-triggered controlled BCNs with impulsive effects. Finally, a biological example is given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]