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H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information
IEEE Transactions on Circuits and Systems I: Regular Papers ( IF 5.1 ) Pub Date : 2021-02-01 , DOI: 10.1109/tcsi.2020.3034897
Hao Shen , Mengping Xing , Shengyuan Xu , Michael V. Basin , Ju H. Park

In this paper, the $\mathcal {H}_{\infty }$ stabilization problem is studied for discrete-time semi-Markov jump singularly perturbed systems (SMJSPSs) with repeated scalar nonlinearities. As the exact statistical information of the sojourn time or the mode transition is difficult to obtain, the case with only partial semi-Markov kernel information available is considered. Furthermore, introducing an external disturbance or nonlinearity into the analysis of discrete-time semi-Markov jump systems (DTSMJSs) meets critical obstacles, since the relation between the system state vectors at two nonadjacent instants is difficult to determine. To address this issue, the variation trend of the Lyapunov function for a semi-Markov jump sequence is analyzed in detail. Subsequently, criteria of mean-square exponential stability (MSES) for DTSMJSs are established for the first time based on the Lyapunov stability theory. By virtue of the criteria obtained and the cone complementary linearization algorithm, a controller ensuring MSES and $\mathcal {H}_{\infty }$ performance for discrete-time nonlinear SMJSPSs is constructed. Finally, the effectiveness and applicability of the proposed method are validated by simulation examples including an inverted pendulum model.

中文翻译:

半马尔可夫核信息部分已知的离散时间非线性半马尔可夫跳跃奇异摄动系统的H∞稳定性

在本文中, $\mathcal {H}_{\infty }$ 研究了具有重复标量非线性的离散时间半马尔可夫跳跃奇异摄动系统 (SMJSPS) 的稳定性问题。由于停留时间或模式转换的准确统计信息难以获得,因此考虑只有部分半马尔可夫核信息可用的情况。此外,在离散时间半马尔可夫跳跃系统 (DTSMJS) 的分析中引入外部干扰或非线性会遇到关键障碍,因为两个不相邻时刻的系统状态向量之间的关系难以确定。针对这个问题,详细分析了半马尔可夫跳跃序列的Lyapunov函数的变化趋势。随后,基于李雅普诺夫稳定性理论,首次建立了 DTSMJS 的均方指数稳定性 (MSES) 准则。凭借获得的准则和锥互补线性化算法,控制器确保 MSES 和 $\mathcal {H}_{\infty }$ 构造了离散时间非线性 SMJSPS 的性能。最后,通过包括倒立摆模型在内的仿真实例验证了所提出方法的有效性和适用性。
更新日期:2021-02-01
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