A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization

Zhao, Shouwei

doi:10.1063/1.3594046

Cited by 8 publications

(2 citation statements)

References 24 publications

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“…In the past decades, the study of synchronisation phenomena has been an active research area in control loop (Liu, Wang, Liang, & Liu, 2009;Lu, Ho, & Cao, 2010;Zhao, 2011). Recently, interest has extended to the synchronisation of Boolean networks for both theoretical and practical reasons.…”

Section: Introductionmentioning

confidence: 98%

Feedback control design for the complete synchronisation of two coupled Boolean networks

2015

International Journal of Systems Science

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In the literatures, to design state feedback controllers to make the response Boolean network synchronise with the drive Boolean network is rarely considered. Motivated by this, feedback control design for the complete synchronisation of two coupled Boolean networks is investigated in this paper. A necessary condition for the existence of a state feedback controller achieving the complete synchronisation is established first. Then, based on the necessary condition, the feedback control law is proposed. Finally, an example is worked out to illustrate the proposed design procedure.

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Section: Introductionmentioning

confidence: 98%

Feedback control design for the complete synchronisation of two coupled Boolean networks

2015

International Journal of Systems Science

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“…Furthermore, discrete switched impulsive system characteristic of certain impulses at switching instants, have been extensively used to describe systems in various applications including information science, electronics and automatic control systems [18,19]. Hence, discrete hybrid systems are much more complex than time-varying discrete systems for which there is a definite mode at any given instant.…”

Section: Introductionmentioning

confidence: 99%

Geometric approach for observability and accessibility of discrete‐time non‐linear switched impulsive systems

Zhao

2013

IET Control Theory & Applications

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This study is concerned with observability and accessibility of discrete-time non-linear switched impulsive systems, for which the problem is more complicated than that for general discrete systems and has novel features. A new method from the combination of differential geometric theory and Lie group analysis is developed. Specifically, under the geometric framework of the system, infinitesimal invariance for the observability and accessibility is investigated, respectively. Based on the invariance investigation, explicit criteria for local observability and local accessibility are derived. Numerical examples are discussed to show the effectiveness of the proposed methods, and the features of observability and accessibility for discrete switched impulsive systems. NomenclatureLet Z + be the set of positive integer. x(k), y(k) and u(k) are n x −, n y − and n u −dimensional vectors, respectively. Denote J = {τ k |k ∈ Z + } ⊆ Z + to be the sequence of impulsive instants satisfying τ 1 < τ 2 < · · · < τ k < · · · , τ k+1 − τ k ≥ 2 and lim k→∞ τ k = ∞. Let J 1 = {1, 2, . . . , N }.

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Partial synchronization in stochastic dynamical networks with switching communication channels

Huang

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, the partial synchronization problem of stochastic dynamical networks (SDNs) is investigated. Unlike the existing models, the SDN considered in this paper suffers from a class of communication constraint-only part of nodes' states can be transmitted. Thus, less nodes' states can be used to synchronize the SDN, which makes the analysis of the synchronization problem much harder. A set of channel matrices are introduced to reflect such kind of constraint. Furthermore, due to unpredictable environmental changes, the channel matrices can switch among some communication modes. The switching considered here is governed by a Markov process. To overcome the difficulty, a regrouping method is employed to derive our main results. The obtained conditions guarantee that partial synchronization can be achieved for SDNs under switching communication constraint. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results and how the communication constraint influences synchronization result.

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A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization

Cited by 8 publications

References 24 publications

Feedback control design for the complete synchronisation of two coupled Boolean networks

Feedback control design for the complete synchronisation of two coupled Boolean networks

Geometric approach for observability and accessibility of discrete‐time non‐linear switched impulsive systems

Partial synchronization in stochastic dynamical networks with switching communication channels

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