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中立型半马尔科夫跳跃系统的可达集边界估计
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Abstract:
中立型半马尔科夫跳跃系统是许多动态系统中存在的时滞系统的一种特殊情况，其可达集估计问题具有理论和实践意义。研究的是具有实变时滞的中立型半马尔科夫跳跃系统的可达集边界问题。首先，构造新的李雅普诺夫泛函，利用Ito引理和Jensen不等式等矩阵不等式技巧，得到了一个较小的可达集边界。其次，用Matlab中的LMI控制工具箱对理论结果进行验证。最后，给出数值案例，说明结果的有效性。
Neutral semi-Markov jump systems are a special case of time-delay systems in many dynamical systems, and the problem of the reachable set estimation has significance in theory and practice. In this paper, the reachable set problem for neutral semi-Markov jump systems with time-varying delays is considered. Firstly, the Lyapunov function is constructed, the no-ellipsoidal bound of the reachable set is as small as what is obtained by applied Ito’s Lemma and Jensen's inequality. Secondly, the LMI toolbox, in Matlab, is used to check the correctness of the results. Finally, numerical examples are given to verify the validity.
| [1] | 罗邦. 一类中立型马尔科夫跳跃系统的稳定性研究[D]: [硕士学位论文]. 贵阳: 贵州民族大学, 2019. |
| [2] | Hou, T., Liu, Y. and Deng, F.Q. (2021) Stability for Discrete-Time Uncertain Systems with Infinite Markov Jump and Time-Delay. Science China (Information Sciences), 64, 100-110. https://doi.org/10.1007/s11432-019-2897-9 |
| [3] | 李娟. 中立型马尔科夫跳跃系统的动力学性质研究[D]: [硕士学位论文]. 贵阳: 贵州民族大学, 2020. |
| [4] | Tao, R.F., Ma, Y.C. and Wang, C.J. (2020) Stochastic Admissibility of Singular Markov Jump Systems with Time-Delay via Sliding Mode Approach. Applied Mathematics and Computation, 380, Article ID: 125282.
https://doi.org/10.1016/j.amc.2020.125282 |
| [5] | Kim, S.H. (2017) Stochastic Stability and Stabilization Conditions of Semi-Markovian Jump Systems with Mode Transition-Dependent Sojourn-Time Distributions. Information Sciences, 385-386, 314-324.
https://doi.org/10.1016/j.ins.2017.01.008 |
| [6] | Li, F. and Shen, H. (2015) Finite-Time H∞ Synchronization Control Semi-Markov Jump Delay Delayed Neural Networks with Randomly Occurring Uncertainties. Neurocomputing, 166, 447-454.
https://doi.org/10.1016/j.neucom.2015.03.034 |
| [7] | Li, L., Qi, W., Chen, X. and Kao, Y. (2018) Stability Analysis and Control Synthesis for Positive Semi-Markov Jump Systems with Time-Varying Delay. Applied Mathematics and Computation, 332, 363-375.
https://doi.org/10.1016/j.amc.2018.02.055 |
| [8] | Zhang, L., Leng, Y. and Colaneri, P. (2015) Stability and Stabilization of Discrete-Time Semi-Markov Jump Linear Systems via Semi-Markov Kernel Approach. IEEE Transactions on Automatic Control, 61, 503-508.
https://doi.org/10.1109/TAC.2015.2438424 |
| [9] | Saporta, B. and Costa, E.F. (2014) Approximate Kalman-Bucy Filter for Continuous-Time Semi-Markov Jump Linear Systems. IEEE Transactions on Automatic Control, 61, 2035-2048. https://doi.org/10.1109/TAC.2015.2495578 |
| [10] | Yu, H., Ma, Y., Liu, J. and Fu, L. (2021) Extended Dissipative Analysis for t-s Fuzzy Semi-Markov Jump Systems with Sampled-Data Input and Actuator Fault. Nonlinear Analysis Hybrid Systems, 40, Article ID: 101010.
https://doi.org/10.1016/j.nahs.2020.101010 |
| [11] | Wang, J.M., Ma, S. and Zhang, C.H. (2016) Stability Analysis and Stabilization for Nonlinear Continuous-Time Descriptor Semi-Markov Jump Systems. Applied Mathematics and Computation, 279, 90-102.
https://doi.org/10.1016/j.amc.2016.01.013 |
| [12] | Li, Q., Liu, X.Z., Zhu, Q.X., Zhong, S.M. and Cheng, J. (2019) Stochastic Synchronization of Semi-Markovian Jump Chaotic Lure Systems with Packet Dropouts Subject to Multiple Sampling Periods. Journal of the Franklin Institute, 356, 6899-6925. https://doi.org/10.1016/j.jfranklin.2019.06.005 |
| [13] | Kim, J.H. (2016) Further Improvement of Jensen Inequality and Application to Stability of Time-Delayed Systems. Automatica, 64, 121-125. https://doi.org/10.1016/j.automatica.2015.08.025 |
| [14] | Qin, J.H., Fu, W.M., Zheng, W.X. and Gao, H.J. (2016) On the Bipartite Consensus for Generic Linear Multiagent Systems with Input Saturation. IEEE Transactions on Cybernetics, 47, 1948-1958.
https://doi.org/10.1109/TCYB.2016.2612482 |
| [15] | 邱枭楠, 张久星, 李颖晖, 李晓华, 董泽洪. 基于可达集的飞机着陆动力学边界保护研究[J]. 电光与控制, 2021, 28(8): 77-81. |
| [16] | 沈长春. 中立型系统的稳定性与可达集边界[M]. 成都: 西南交通大学出版社, 2015: 1-208. |
| [17] | 沈长春. 时滞中立型系统的动力学问题研究[D]: [博士学位论文]. 成都: 电子科技大学, 2012. |
| [18] | 张航, 王天波, 丁阳. 基于滑模控制的不确定中立型系统有限时间稳定[J/OL]. 信息与控制, 2021, 28(8): 1-7. |
| [19] | Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V. (1994) Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia. https://doi.org/10.1137/1.9781611970777 |
| [20] | Skorokhod, A.V. (1989) Asymptotic Methods in the Theory of Stochastic Differential Equation. American Mathematical Society, Providence. |
| [21] | Seuret, A. and Gouaisbaut, F. (2013) Wirtinger-Based Integral Inequality: Application to Time-Delay Systems. Automatica, 49, 2860-2866. https://doi.org/10.1016/j.automatica.2013.05.030 |
