Guaranteed Cost for an Event-Triggered Consensus Strategy for Interconnected Two Time-Scales Systems With Structured Uncertainty.

This article proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states, respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems' dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Impulsive Multisynchronization of Coupled Multistable Neural Networks With Time-Varying Delay.

This paper studies the synchronization problem of coupled delayed multistable neural networks (NNs) with directed topology. To begin with, several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points. Then two new concepts named dynamical multisynchronization (DMS) and static multisynchronization (SMS) are introduced to describe the two novel kinds of synchronization manifolds. Using the impulsive control strategy and the Razumikhin-type technique, some sufficient conditions for both the DMS and the SMS of the controlled coupled delayed multistable NNs with fixed and switching topologies are derived, respectively. Simulation examples are presented to illustrate the effectiveness of the proposed results.

Global synchronization of complex dynamical networks through digital communication with limited data rate.

This paper studies the global synchronization of complex dynamical network (CDN) under digital communication with limited bandwidth. To realize the digital communication, the so-called uniform-quantizer-sets are introduced to quantize the states of nodes, which are then encoded and decoded by newly designed encoders and decoders. To meet the requirement of the bandwidth constraint, a scaling function is utilized to guarantee the quantizers having bounded inputs and thus achieving bounded real-time quantization levels. Moreover, a new type of vector norm is introduced to simplify the expression of the bandwidth limit. Through mathematical induction, a sufficient condition is derived to ensure global synchronization of the CDNs. The lower bound on the sum of the real-time quantization levels is analyzed for different cases. Optimization method is employed to relax the requirements on the network topology and to determine the minimum of such lower bound for each case, respectively. Simulation examples are also presented to illustrate the established results.

Synchronization of continuous dynamical networks with discrete-time communications.

In this paper, synchronization of continuous dynamical networks with discrete-time communications is studied. Though the dynamical behavior of each node is continuous-time, the communications between every two different nodes are discrete-time, i.e., they are active only at some discrete time instants. Moreover, the communication intervals between every two communication instants can be uncertain and variable. By choosing a piecewise Lyapunov-Krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique, a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained. The results extend and improve upon earlier work. Simulation results show the effectiveness of the proposed communication scheme. Some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network, a star-like network, and a nearest neighbor network.

Impulsive control for synchronization of a class of continuous systems.

An impulsive control theory for synchronization of a class of continuous systems is developed. A sufficient condition for the impulsive control is derived. The proposed impulsive control scheme is illustrated by some continuous chaotic systems and the simulation results demonstrate the effectiveness of the method.