The Equalibrium Points of Control Systems with Single Saturate Input under Commuting Matrices

Acta Scientiarum Naturalium Universitatis Pekinensis

Previous Articles Next Articles

The Equalibrium Points of Control Systems with Single Saturate Input under Commuting Matrices

GUO Shuli，HUANG Lin，CHU Tianguang

Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, 100871

Received:2000-11-21 Online:2002-01-20 Published:2002-01-20

在状态阵可交换下单输入饱和系统的平衡点的判别

郭树理,黄琳,楚天广

北京大学力学与工程科学系，系统与控制中心，北京，100871

Abstract

Abstract: The equilibrium points of control systems with saturated inputs are defined. Based on these definitions, all kinds of the equilibrium points are analyzed in control systems with single saturated input. By the above facts, it is necessary in analyzing globally asymptotical stability of the origin that the other asymptotical stability equilibrium points are false ones.

Key words: single saturated input, true equilibrium points, false equilibrium points, commuting matrices, stability, asymptotical stability

摘要： 首先引入了饱和系统平衡点的分类。在此基础上，论证了单饱和输入下，开环，闭环均稳定或其一稳定时的平衡点的分布规律及判别准则；最后指出，当原点全局渐近稳定时，其余非零稳定平衡点均为伪平衡点的必要性。

关键词: 单饱和输入, 真平衡点, 伪平衡点, 可交换, 稳定, 渐近稳定

CLC Number:

O317

GUO Shuli,HUANG Lin,CHU Tianguang. The Equalibrium Points of Control Systems with Single Saturate Input under Commuting Matrices[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

郭树理,黄琳,楚天广. 在状态阵可交换下单输入饱和系统的平衡点的判别[J]. 北京大学学报（自然科学版）.

[1]	YANG Xingwen, YONG Shanshan, WANG Xin’an, ZHOU Kangsheng, JIN Xiuru. Design and Implementation of Data Acquisition System for AETA [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2020, 56(4): 600-606.
[2]	LIAO Hanru, Indree Tuvshintogtokh, GUO Tong, ZHAO Jingxue. Effects of Grazing Exclusion on the Vegetation Community Composition and the Community Stability of Dry Steppe and Mountain Steppe Ecosystems in Mongolia [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2020, 56(3): 471-478.
[3]	WANG Shu, LIU Shuhua, CHEN Jianzhou, HU Ju, FENG Shuanglei, MA Yulong, MIAO Yucong. Case Studies: Simulation on Characteristics of Wind Turbine Wake Effect in a Lake-Side Wind Farm with WRF-Fitch [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2018, 54(3): 605-615.
[4]	MEI Fengxiang,WU Huibin,LI Yanmin. Two Kinds of Gradient Representations for Nielsen Equations [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2016, 52(4): 588-591.
[5]	YUE Baozeng, YAN Yulong. Stability Analysis of Rigid-Liquid-Flexible Coupling Dynamics of Spacecraft Systems by Using the Energy-Casimir Method [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2016, 52(4): 608-618.
[6]	XIAO Shifu, CHEN Xueqian, LIU Xinen. Study on the Vibration Characteristic and Axial-Compressive Stability of the Beam with Simple and Flexible Supports [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2016, 52(4): 699-707.
[7]	YIN Youquan,DI Yuan. On the Instability of Engineering Rock-Like Materials [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2014, 50(6): 991-997.
[8]	LI Lili,HU Xuan,YANG Shunshun,LUAN Shengji. Evolutionary Game Analysis on Environmental Cooperation of Rural Households [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2014, 50(5): 935-941.
[9]	ZHANG Boya,YANG Ting,HU Xia,ZHANG Jianbo. Characteristic of the Cellulose Immobilized on Aminated SiO₂ [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2014, 50(5): 965-968.
[10]	WANG Yanhui,LIU Shuqin,DONG Taiqian. A New Way to Make the Absorption Cell of Rb Frequency Standard [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2011, 47(2): 370-372.
[11]	KANG Ling,ZHANG Hongsheng,WANG Zhiyuan,CHEN Jiayi. Study on the Atmospheric Stability Class over Different Surface Conditions [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2011, 47(1): 66-70.
[12]	FENG Wangsen,CHEN Ping,ZHANG Bei. Stability Analysis of a P2P Overlay Maintenance Protocol [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2009, 45(4): 589-593.
[13]	YIN Youquan,CHEN Zhaowei. Study on Wellbore Collapse Using the Theory and Method of Stability [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2009, 45(4): 559-564.
[14]	CAO Bao,QIN Qiming,LI Baishou,ZHANG Zexun,ZHANG Zili. Day and Night Alternation of Natural Ultra-Low Frequency Electromagnetic Field and Its Stability Analysis [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2008, 44(6): 897-901.
[15]	YANG Guang ,ZHANG Jianbo,WANG Shanlin ,YANG Yuxiang ,ZONG Yueru,WANG Weijing. Condition and Effect of Reactor for Removal of Pentachlorophenol Catalyzed by Immobilized HRP [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2008, 44(2): 233-236.

The Equalibrium Points of Control Systems with Single Saturate Input under Commuting Matrices

在状态阵可交换下单输入饱和系统的平衡点的判别

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics