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Stochastic stability of Markovian jump linear systems over networks with random quantization density and time delay

Author

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  • Wang, Jufeng
  • Zhou, MengChu
  • Liu, Chunfeng

Abstract

This work studies the stochastic stability of Markovian jump linear systems in a communication network-based environment. By modeling quantization density as well as the sensor-to-controller and controller-to-actuator delays as Markov chains, the closed-loop networked control systems are expressed as switched linear systems. The necessary and sufficient conditions of stochastic stability are derived. By solving a set of linear matrix inequalities with matrix inversion constraints, this work presents a three-mode-dependent state-feedback controller. Its control performance is illustrated via a numerical example.

Suggested Citation

  • Wang, Jufeng & Zhou, MengChu & Liu, Chunfeng, 2018. "Stochastic stability of Markovian jump linear systems over networks with random quantization density and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1128-1139.
    • Handle: RePEc:eee:phsmap:v:509:y:2018:i:c:p:1128-1139
    DOI: 10.1016/j.physa.2018.06.074
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    References listed on IDEAS

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    1. Sun, Mingmei & Xu, Meng, 2017. "Exponential stability and interval stability of a class of stochastic hybrid systems driven by both Brownian motion and Poisson jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 58-73.
    2. Huber, Greg & Pradas, Marc & Pumir, Alain & Wilkinson, Michael, 2018. "Persistent stability of a chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 517-523.
    3. Jin, Yanfei & Xu, Meng, 2016. "Stability analysis in a car-following model with reaction-time delay and delayed feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 107-116.
    4. Liu, Chao & Wang, Luping & Zhang, Qingling & Yan, Yun, 2017. "Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 682-698.
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