Synchronization:a universal concept in nonlinear science

In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected.

Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems

In this paper, global exponential synchronization stability in an array of linearly diffusively coupled reaction-diffusion neural networks with time-varying delays is investigated by adding impulsive controller to a small fraction of nodes (pinning-impulsive controller). In order to overcome the difficulty resulting from the fact that the impulsive controller affects only the dynamical behaviors of the controlled nodes, a new analysis method is developed. By using the developed method, two known lemmas on stability of delayed functional differential equation with and without impulses, and Lyapunov stability theory, several novel and easily verified synchronization criteria guaranteeing the whole network will be pinned to a homogenous solution are derived. Moreover, the effects of the pinning-impulsive controller and the dynamics of the uncontrolled nodes and the diffusive couplings on the synchronization process are explicitly expressed in the obtained criteria. Our results also show that we can always de...

Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

New Results on Output Feedback $H_{\infty} $ Control for Linear Discrete-Time Systems

In this paper, the global exponential synchronization of delayed complex dynamical networks with nonidentical nodes and stochastic perturbations is studied. By combining adaptive control and impulsive control schemes, the considered network can be synchronized onto any given goal dynamics. The adaptive control is discontinuous and can overcome the unknown difference between dynamical nodes and goal system. As for the impulsive control, the concept named “average impulsive interval” with “elasticity number” of impulsive sequence is utilized to get less conservative synchronization criterion. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.

Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control

Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints

This paper studies the hidden dynamics of a class of two-dimensional maps inspired by the Henon map. A special consideration is made to the existence of fixed points and their stabilities in these maps. Our concern focuses on three typical scenarios which may generate hidden dynamics, i.e., no fixed point, single fixed point, and two fixed points. A computer search program is employed to explore the strange hidden attractors in the map. Our findings show that the basins of some hidden attractors are tiny, so the standard computational procedure for localization is unavailable. The schematic exploring method proposed in this paper could be generalized for investigating hidden dynamics of high-dimensional maps.

/pdf/hidden-chaotic-attractors-in-a-class-of-two-dimensional-maps-7gtt8d0yf2.pdf

Hidden chaotic attractors in a class of two-dimensional maps

http://image.sciencenet.cn/olddata/kexue.com.cn/upload/blog/file/2010/8/201085102931775587.pdf

Impulsive synchronization of networked nonlinear dynamical systems

In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.

Consensus of multi-agent linear dynamic systems via impulsive control protocols

Robust local and global hybrid adaptive and impulsive synchronisation for a class of uncertain complex dynamical networks are investigated in this study, respectively. For the complex dynamical network with unknown but bounded non-linear couplings, with unknown bounds, hybrid adaptive and impulsive controllers are designed based on adaptive control theory and impulsive control theory. By the generalised Barbalat's lemma, the uncertain complex dynamical network is proved to be locally or globally asymptotically synchronised. Several robust local and global hybrid adaptive and impulsive synchronisation criteria are also established. Two numerical examples are given to demonstrate the effectiveness of the proposed controller design methods.

Haibo Jiang

Papers

Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints

Hidden chaotic attractors in a class of two-dimensional maps

Impulsive synchronization of networked nonlinear dynamical systems

Consensus of multi-agent linear dynamic systems via impulsive control protocols

Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical networks by the generalised Barbalat's lemma