具有量化误差的多步长非线性采样系统的镇定

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 13-26.

具有量化误差的多步长非线性采样系统的镇定

余宏旺¹, 汪志鸣^2,3, 张宝善¹

1.南京审计学院数学与统计学院南京 211815;
2.华东师范大学数学系上海 200241;
3.华东师范大学数学系应用数学与交叉科学中心上海 200062

收稿日期:2009-09-08 修回日期:2011-12-06 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
国家自然科学基金(10671069)、上海市重点学科项目(B407)和南京审计学院微分方程理论与应用硕士点建设基金(202720035)资助

Stabilization of Multi-rate Sampled-data Nonlinear Systems with Quantization

YU Hong-Wang¹, WANG Zhi-Ming^2,3, ZHANG Bao-Shan¹

1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing 211815;
2.Department of Mathematics, East China Normal University, Shanghai 200241;
3.Center for Applied and Interdisciplinary Mathematics, Department of Mathematics, East China Normal University, Shanghai 200062

Received:2009-09-08 Revised:2011-12-06 Online:2012-02-25 Published:2012-02-25
Supported by:
国家自然科学基金(10671069)、上海市重点学科项目(B407)和南京审计学院微分方程理论与应用硕士点建设基金(202720035)资助

摘要/Abstract

摘要：

该文研究一类非线性控制系统在采样器采样过程中产生量化误差的情况下多步长采样镇定问题. 运用近似DTD方法, 在非线性系统的近似离散时间模型上设计全局状态反馈镇定控制器. 当系统近似误差和采样量化误差被限制在一定的条件下, 可以得到含量化误差的多步长非线性采样系统是半全局实用渐近稳定. 最后, 仿真例子验证了所得结果的有效性.

关键词: 多步长采样, 量化误差, 半全局实用渐近稳定

Abstract:

This paper investigates multi-rate sampled-data stabilization of nonlinear control systems while the sampler produces quantization during sampling. The approximate DTD method is employed to design a (globally) stabilized controller based on the approximate discrete-time models of the nonlinear plant. It is shown that the multi-rate sampled-data nonlinearcontrolsystemswith quantizationareguaranteedtobe semi-globallypracticalasymp-totically stable while the approximate error and quantization level are restricted by a certain error condition. A simulation example illustrates the validity of obtained results.

Key words: Multi-rate sampled-data, Quantization, Semi-globally practically asymptotic sta-bility

中图分类号:

93C57

余宏旺, 汪志鸣, 张宝善. 具有量化误差的多步长非线性采样系统的镇定[J]. 数学物理学报, 2012, 32(1): 13-26.

YU Hong-Wang, WANG Zhi-Ming, ZHANG Bao-Shan. Stabilization of Multi-rate Sampled-data Nonlinear Systems with Quantization[J]. Acta mathematica scientia,Series A, 2012, 32(1): 13-26.

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