Robust Stability, Stabilization, and H-infinity Control of a Class of Nonlinear Discrete Time Stochastic Systems

Zhang Tianliang; Wang Yu-Hong; Jiang Xiushan; Zhang Weihai

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Robust Stability, Stabilization, and H-infinity Control of a Class of Nonlinear Discrete Time Stochastic Systems

机译：一类非线性离散时间随机系统的鲁棒稳定性，镇定和H∞控制

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This paper studies robust stability, stabilization, and H-infinity control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robust H-infinity state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robust H-infinity performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.

机译：本文研究了一类非线性离散时间随机系统的鲁棒稳定性，镇定性和H∞控制。首先，通过线性矩阵不等式（LMI）获得了易于测试的随机稳定性和随机稳定性标准。然后，设计了一种鲁棒的H-无限状态反馈控制器，这样所涉及的系统不仅可以在内部随机稳定，而且还可以满足鲁棒的H-无限性能。此外，将非线性扰动的离散随机系统的先前结果推广到同时具有状态，控制和外部干扰相关噪声的系统。给出两个数值例子来说明所提出结果的有效性。

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来源
《Mathematical Problems in Engineering》 |2016年第4期|5185784.1-5185784.11|共11页
作者
Zhang Tianliang; Wang Yu-Hong; Jiang Xiushan; Zhang Weihai;
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China Univ Petr East China, Coll Informat & Control Engn, Qingdao 266510, Shandong, Peoples R China;

China Univ Petr East China, Coll Informat & Control Engn, Qingdao 266510, Shandong, Peoples R China;

China Univ Petr East China, Coll Informat & Control Engn, Qingdao 266510, Shandong, Peoples R China;

Shandong Univ Sci & Technol, Coll Elect Engn, Qingdao 266590, Shandong, Peoples R China;

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1. Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays [J] . Shuang Liang, Yali Dong Journal of control science and engineering . 2016,第pta1期

机译：一类具有时变时滞的不确定非线性离散时间随机系统的鲁棒稳定性和镇定
2. Robust stability and stabilization of a class of nonlinear discrete time stochastic systems: An LMI approach [J] . Sathananthan S., Knap M.J., Strong A., Applied mathematics and computation . 2012,第4期

机译：一类非线性离散时间随机系统的鲁棒稳定性和稳定性：一种LMI方法
3. ROBUST STABILITY AND ROBUST STABILIZATION OF A CLASS OF DISCRETE-TIME TIME-VARYING LINEAR STOCHASTIC SYSTEMS [J] . Aberkane Samir, Dragan Vasile SIAM Journal on Control and Optimization . 2015,第1期

机译：一类离散时变线性随机系统的鲁棒稳定性和鲁棒镇定。
4. Stability and Stabilization for Nonlinear Discrete-time Singular Markov Jump Systems with Time-varying Delay Stability and Stabilization for Nonlinear Discrete-time Singular Markov Jump Systems with Time-varying Delay [C] . Rui Wang, Shuping Ma Chinese Control and Decision Conference . -1

机译：时滞非线性离散时间奇异Markov跳跃系统的稳定性和镇定
5. Robust Stability and Stabilization of a Class of Non-Linear Discrete-Time Stochastic Systems. [D] . Strong, Andre' J. 2011

机译：一类非线性离散时间随机系统的鲁棒稳定性和稳定性。
6. Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay [O] . Tengyu Ma, Longsuo Li -1

机译：具有时滞的不确定中立随机非线性系统的时滞相关鲁棒稳定性的稳定性判据
7. Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays [O] . Shuang Liang, Yali Dong 2016

机译：间隔时变延迟一类不确定非线性离散时间随机系统的鲁棒稳定性和稳定性
8. Stability of a Class of Discrete Time Systems with a Single Feedback Nonlinearity. [R] . Narendra, K. S., Neuman, C. P. 1965

机译：一类具有单反馈非线性的离散时间系统的稳定性。

Robust Stability, Stabilization, and H-infinity Control of a Class of Nonlinear Discrete Time Stochastic Systems

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