Stabilization of Aperiodic Sampled-Data Boolean Control Networks: A Delay Approach

• 成果类型: Article
• 署名作者: Sun, Liangjie; Ching, Wai-Ki; Lu, Jianquan
• 署名单位: University of Hong Kong; Southeast University - China; Chengdu University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3055191
• 发表日期: 2021
• 页码: 5606-5611
• 关键词: Delays; stability analysis; Matrix converters; Random variables; Lyapunov methods; Upper bound; sun; Aperiodic sampled-data control (ASDC); Boolean control networks (BCNs); time-varying delay

摘要

In this article, a novel method for the global stochastic stability analysis of aperiodic sampled-data Boolean control networks (BCNs) is introduced. In our article, the sampling instants of aperiodic sampled-data control (ASDC) are uncertain and only the activation frequencies of the sampling interval are known. Using the semitensor product of matrices, a BCN under ASDC can be transformed into a Boolean network (BN) with stochastic delays. Specifically, the ASDC is represented as a delayed control. Here, the time-varying delay is a random variable generated by a Markov chain and its transition probability matrix can be obtained by the activation frequencies of the sampling interval. Notably, the value of the time-varying delay is less than the upper bound of the sampling interval and when its present value is given, there are only two possible values that can be taken at the next moment. Subsequently, by using the Lyapunov function and augmented method, a sufficient condition for the global stochastic stability of BCNs under ASDC is provided. In particular, the aforementioned results are applicable to the sampled-data control with constant sampling interval. Finally, a numerical example is presented to demonstrate our results.