Stability and ℓ₁-gain analysis for positive 2-D Markov jump systems

References

• Anderson, B., Agathoklis, P., Jury, E., & Mansour, M. (1986). Stability and the matrix Lyapunov equation for discrete 2-dimensional systems. IEEE Transactions on Circuits and Systems, 33(3), 261–267. doi: 10.1109/TCS.1986.1085912
   Google Scholar
• Benzaouia, A., Hmamed, A., Tadeo, F., & Hajjaji, A. E. (2011). Stabilisation of discrete 2D time switched systems by state feedback control. International Journal of Systems Science, 42(3), 479–487. doi: 10.1080/00207720903576522
   Web of Science ®Google Scholar
• Chen, X., Lam, J., Li, P., & Shu, Z. (2013). ℓ1-induced norm and controller synthesis of positive systems. Automatica, 49(5), 1377–1385. doi: 10.1016/j.automatica.2013.02.023
   Web of Science ®Google Scholar
• Chen, X., Lam, J., & Meng, M. (2017). Controller synthesis for positive Takagi-Sugeno fuzzy systems under ℓ1 performance. International Journal of Systems Science, 48(3), 515–524. doi: 10.1080/00207721.2016.1188176
   Web of Science ®Google Scholar
• Costa, O. L. V., Fragoso, M. D., & Marques, R. P. (2005). Discrete-time Markov jump linear systems. London: Springer-Verlag.
   Google Scholar
• Du, S., Qiao, J., Zhao, X., & Wang, R. (2018). Stability and ℓ1-gain analysis for switched positive T-S fuzzy systems under asynchronous switching. Journal of the Franklin Institute, 355(13), 5912–5927. doi: 10.1016/j.jfranklin.2018.06.005
   Web of Science ®Google Scholar
• Du, C., Xie, L., & Zhang, C. (2001). H∞ control and robust stabilization of two-dimensional systems in Roesser models. Automatica, 37(2), 205–211. doi: 10.1016/S0005-1098(00)00155-2
   Web of Science ®Google Scholar
• Duan, Z., & Xiang, Z. (2014). H2 output feedback controller design for discrete-time 2D switched systems. Transactions of the Institute of Measurement and Control, 36(1), 68–77. doi: 10.1177/0142331213485279
   Google Scholar
• Fei, Z., Shi, S., Zhao, C., & Wu, L. (2017). Asynchronous control for 2-D switched systems with mode-dependent average dwell time. Automatica, 79, 198–206. doi: 10.1016/j.automatica.2017.01.026
   Web of Science ®Google Scholar
• Fornasini, E., & Marchesini, G. (1976). State-space realization theory of two-dimensional filters. IEEE Transactions on Automatic Control, 21(4), 484–492. doi: 10.1109/TAC.1976.1101305
   Web of Science ®Google Scholar
• Fornasini, E., & Marchesini, G. (1978). Double indexed dynamical systems. Mathematical Systems Theory, 12, 59–72. doi: 10.1007/BF01776566
   Google Scholar
• Fornasini, E., & Valcher, M. E. (2005). Controllability and reachability of 2-D positive systems: A graph theoretic approach. IEEE Transactions on Circuits and Systems (I), 52(3), 576–585. doi: 10.1109/TCSI.2004.842872
   Google Scholar
• Gao, H., Lam, J., Xu, S., & Wang, C. (2004). Stabilization and H∞ control of two-dimensional Markovian jump systems. IMA Journal of Mathematical Control and Information, 21(4), 377–392. doi: 10.1093/imamci/21.4.377
   Google Scholar
• Hernandez-Vargas, E. A., Colaneri, P., & Middleton, R. H. (2014). Switching strategies to mitigate HIV mutation. IEEE Transactions on Control Systems Technology, 22(4), 1623–1628. doi: 10.1109/TCST.2013.2280920
   Web of Science ®Google Scholar
• Hinamoto, T. (1997). Stability of 2-D discrete systems described by the Fornasini-Marchesini second model. IEEE Transactions on Circuits and Systems (I), 44(3), 254–257. doi: 10.1109/81.557373
   Google Scholar
• Kaczorek, T. (2007). The choice of the forms of Lyapunov functions for a positive 2D Roesser model. International Journal of Applied Mathematics and Computer Science, 17(4), 471–475. doi: 10.2478/v10006-007-0039-7
   Web of Science ®Google Scholar
• Kaczorek, T. (2009). Asymptotic stability of positive 2D linear systems with delays. Bulletin of the Polish Academy of Sciences: Technical Sciences, 57(2), 133–138. doi: 10.2478/v10175-010-0113-4
   Web of Science ®Google Scholar
• Kaczorek, T. (2011). New stability tests of positive 1D and 2D linear systems. In Proceeding of 25th European conference modelling and simulation, Krakow, Poland (pp. 237–243).
   Google Scholar
• Kaczorek, T. (2012). Positive 1D and 2D systems. London: Springer-Verlag.
   Google Scholar
• Kurek, J. E. (2002). Stability of positive 2-D system described by the Roesser model. IEEE Transactions on Circuits and Systems (I), 49(4), 531–533. doi: 10.1109/81.995672
   Google Scholar
• Li, Z., & Lam, J. (2016). Dominant pole and eigenstructure assignment for positive systems with state feedback. International Journal of Systems Science, 47(12), 2901–2912. doi: 10.1080/00207721.2015.1036477
   Web of Science ®Google Scholar
• Lian, J., Liu, J., & Zhuang, Y. (2015). Mean stability of positive Markov jump linear systems with homogeneous and switching transition probabilities. IEEE Transactions on Circuits and Systems II: Express Briefs, 62(8), 801–805. doi: 10.1109/TCSII.2015.2433371
   Web of Science ®Google Scholar
• Liang, J., Pang, H., & Wang, J. (2017). Filtering and ℓ1-gain analysis for 2-D positive system with Markov jump parameters. In 2017 11th Asian control conference, Gold Coast, Australia (pp. 108–113).
   Google Scholar
• Lu, W. S., & Lee, E. (1985). Stability analysis for two-dimensional systems via a Lyapunov approach. IEEE Transactions on Circuits and Systems, 32(1), 61–68. doi: 10.1109/TCS.1985.1085596
   Google Scholar
• Roesser, R. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20(1), 1–10. doi: 10.1109/TAC.1975.1100844
   Web of Science ®Google Scholar
• Shen, J., & Lam, J. (2016). Static output-feedback stabilization with optimal ℓ1-gain for positive linear systems. Automatica, 63, 248–253. doi: 10.1016/j.automatica.2015.10.025
   Google Scholar
• Sun, H., Zhang, Y., & Wu, A. (2018). Stochastic stability analysis of Markovian jump linear systems with incomplete transition descriptions. IET Control Theory & Applications, 12(14), 1974–1982. doi: 10.1049/iet-cta.2017.1445
   Web of Science ®Google Scholar
• Wang, D., Wang, Z., Li, G., & Wang, W. (2016). Distributed filtering for switched nonlinear positive systems with missing measurements over sensor networks. IEEE Sensors Journal, 16(12), 4940–4948. doi: 10.1109/JSEN.2016.2555761
   Web of Science ®Google Scholar
• Wang, J., & Zhao, J. (2017). Output tracking control with ℓ1-gain performance for positive switched systems. Journal of the Franklin Institute, 354(10), 3907–3918. doi: 10.1016/j.jfranklin.2017.03.016
   Google Scholar
• Wei, Y., Qiu, J., Karimi, H. R., & Wang, M. (2015). Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information. Multidimensional Systems and Signal Processing, 26(3), 575–597. doi: 10.1007/s11045-013-0276-x
   Web of Science ®Google Scholar
• Wu, L., Shi, P., Gao, H., & Wang, C. (2008). H∞ filtering for 2D Markovian jump systems. Automatica, 44(7), 1849–1858. doi: 10.1016/j.automatica.2007.10.027
   Web of Science ®Google Scholar
• Wu, L., Yang, R., Shi, P., & Su, X. (2015). Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings. Automatica, 59, 206–215. doi: 10.1016/j.automatica.2015.06.008
   Web of Science ®Google Scholar
• Xiang, Z., & Huang, S. (2013). Stability analysis and stabilization of discrete-time 2D switched systems. Circuits, Systems, and Signal Processing, 32(1), 401–414. doi: 10.1007/s00034-012-9464-4
   Web of Science ®Google Scholar
• Xiang, W., Lam, J., & Shen, J. (2017). Stability analysis and ℓ1-gain characterization for switched positive systems under dwell-time constraint. Automatica, 85, 1–8. doi: 10.1016/j.automatica.2017.07.016
   Web of Science ®Google Scholar
• Yang, R., Xie, L., & Zhang, C. (2006). H2 and mixed H2/H∞ control of two-dimensional systems in Roesser model. Automatica, 42(9), 1507–1514. doi: 10.1016/j.automatica.2006.04.002
   Web of Science ®Google Scholar
• Zhang, J., Jia, X., Zhang, R., & Zuo, Y. (2018). A model predictive control framework for constrained uncertain positive systems. International Journal of Systems Science, 49(4), 884–896. doi: 10.1080/00207721.2017.1419307
   Web of Science ®Google Scholar
• Zhang, L., & Lam, J. (2010). Necessary and sufficient conditions for analysis and synthesis of Markov jump linear systems with incomplete transition descriptions. IEEE Transactions on Automatic Control, 55(7), 1695–1701. doi: 10.1109/TAC.2010.2046607
   Web of Science ®Google Scholar
• Zhu, S., Han, Q., & Zhang, C. (2014). ℓ1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach. Automatica, 50(8), 2098–2107. doi: 10.1016/j.automatica.2014.05.022
   Web of Science ®Google Scholar
• Zhu, S., Wang, B., & Zhang, C. (2017). Delay-dependent stochastic finite-time ℓ1-gain filtering for discrete-time positive Markov jump linear systems with time-delay. Journal of the Franklin Institute, 354(15), 6894–6913. doi: 10.1016/j.jfranklin.2017.07.008
   Web of Science ®Google Scholar