An Algorithm for Labeling Stable Regions of a Class of Time-Delay Systems with Abscissa  

作　　者：Wang Qiang Wang Zaihua 

机构地区：[1]Army Engineering University of PLA,Nanjing 211101,P.R.China [2]State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,P.R.China

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2018年第1期94-100,共7页南京航空航天大学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No.11372354)

摘　　要：Stability is usually in the sense of Lyapunov′s asymptotical stability,thus the solutions starting from points close to a stable equilibrium may have a very long transient.In the applications of time-delayed feedback controls,it is important not only to determine the stable regions in the gain plane or gain space,but also to find out the abscissa that can be used as an index of stability.Based on the D-subdivision method,this paper proposes a simple algorithm for finding and labeling the stable regions in feedback gain plane with abscissa.The labeled sub-regions with smaller abscissa are better in applications.The main results are presented for the controlled pendulum or inverted pendulum under a delayed feedback,and are illustrated with two case studies.Stability is usually in the sense of Lyapunov′s asymptotical stability,thus the solutions starting from points close to a stable equilibrium may have a very long transient.In the applications of time-delayed feedback controls,it is important not only to determine the stable regions in the gain plane or gain space,but also to find out the abscissa that can be used as an index of stability.Based on the D-subdivision method,this paper proposes a simple algorithm for finding and labeling the stable regions in feedback gain plane with abscissa.The labeled sub-regions with smaller abscissa are better in applications.The main results are presented for the controlled pendulum or inverted pendulum under a delayed feedback,and are illustrated with two case studies.

关 键 词：time delay STABILITY Lyapunov′s STABILITY abscissa DELAYED FEEDBACK optimal FEEDBACK gain 

分 类 号：O317[理学—一般力学与力学基础]