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Articles

Stability and stabilisation of Markovian jump systems under fast switching: an averaging approach

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Pages 572-583 | Received 24 Feb 2022, Accepted 19 Sep 2022, Published online: 19 Oct 2022

References

  • Aberkane, S. (2011). Stochastic stabilization of a class of nonhomogeneous Markovian jump linear systems. Systems and Control Letters, 60(3), 156–160. https://doi.org/10.1016/j.sysconle.2010.11.001
  • Bolzern, P., Colaneri, P., & Nicolao, De. G. (2014). Stochastic stability of positive Markov jump linear systems. Automatica, 50(4), 1181–1187. https://doi.org/10.1016/j.automatica.2014.02.016
  • Cheng, J., Zhu, H., & Zhong, S. (2015). Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching. International Journal of Systems Science, 46(6), 1080–1093. https://doi.org/10.1080/00207721.2013.808716
  • Costa, O. L. V., Fragoso, M. D., & Todorov, M. G. (2012). Continuous-time Markov jump linear systems. Springer.
  • Faraji-Niri, M., Jahed-Motlagh, M., & Barkhordari-Yazdi, M. (2014). Stochastic stabilization of uncertain Markov jump linear systems with time varying transition rates. 2014 22nd Iranian conference on electrical engineering (ICEE) (pp. 1186–1191).
  • Feng, Z., & Shi, P. (2017). Sliding mode control of singular stochastic Markov jump systems. IEEE Transactions on Automatic Control, 62(8), 4266–4273. https://doi.org/10.1109/TAC.2017.2687048
  • Gao, X., Ren, H., & Deng, F. (2019). Observer-based finite-time H∞ control for uncertain discrete-time nonhomogeneous Markov jump systems. Journal of the Franklin Institute, 356(4), 1730–1749. https://doi.org/10.1016/j.jfranklin.2018.10.031
  • Hongkeun, K., Hyungbo, S., Juhoon, B., & H. S. Jin (2013). Consensus of output-coupled linear multi-agent systems under fast switching network: Averaging approach. Automatica, 49(1), 267–272. https://doi.org/10.1016/j.automatica.2012.09.025
  • Li, S., & Lian, J. (2021). Almost sure stability of Markov jump systems with persistent dwell time switching. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(11), 6681–6690. https://doi.org/10.1109/TSMC.2020.2964034
  • Li, H., Shi, P., & Yao, D. (2016). Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults. IEEE Transactions on Automatic Control, 62(4), 1933–1939. https://doi.org/10.1109/TAC.2016.2588885
  • Luan, X., Zhao, S., & Liu, F (2013). H∞ control for discrete-time Markov jump systems with uncertain transition probabilities. IEEE Transactions on Automatic Control, 58(6), 1566–1572. https://doi.org/10.1109/TAC.2012.2229839
  • Lutz, C. C., & Stilwell, D. J. (2015). Stability and disturbance attenuation for Markov jump linear systems with time-varying transition probabilities. IEEE Transactions on Automatic Control, 61(5), 1413–1418. https://doi.org/10.1109/TAC.2015.2476196
  • Narendra, K. S., & Tripathi, S. S. (1973). Identification and optimization of aircraft dynamics. Journal of Aircraft, 10(4), 193–199. https://doi.org/10.2514/3.44364
  • Stilwell, D. J., Bollt, E. M., & Roberson, D. G. (2006). Sufficient conditions for fast switching synchronization in time-varying network topologies. SIAM Journal on Applied Dynamical Systems, 5(1), 140–156. https://doi.org/10.1137/050625229
  • Wang, G. L., & Fan, Q. (2020). Stabilization of semi-Markovian jump systems by a stochastically scheduled controller. International Journal of Robust and Nonlinear Control, 31(5), 1621–1639. https://doi.org/10.1002/rnc.v31.5
  • Wang, G. L., & Sun, Y. Y. (2020). Almost sure stabilization of continuous-time jump linear systems via a stochastic scheduled controller. IEEE Transactions on Cybernetics, 52(5), 2712–2724. https://doi.org/10.1109/TCYB.2020.3021424
  • Wang, G. L., & Xu, L. (2020a). Almost sure stability and stabilization of Markovian jump systems with stochastic switching. IEEE Transactions on Automatic Control, 67(3), 1529–1536. https://doi.org/10.1109/TAC.2021.3069705
  • Wang, G. L., & Xu, L. (2020b). Stability and stabilization for singularly perturbed systems with Markovian jumps. International Journal of Robust and Nonlinear Control, 30(12), 4690–4707. https://doi.org/10.1002/rnc.v30.12
  • Wang, G. L., Zhang, Q. L., & Yan, X. G. (2014). Analysis and design of singular Markovian jump systems. Springer.
  • Yao, D., Zhang, B., Li, P., & Li, H. (2019). Event-triggered sliding mode control of discrete-time Markov jump systems. IEEE Transactions on Systems, 49(10), 2016–2025. https://doi.org/10.1109/TSMC.2018.2836390

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