The Relationship Between Periodic Solutions and Stability in a Class of Third-Order Relay Control Systems

作     者：Michaels, Lawrence H. Frederick, Dean K. 

作者机构：Electronic Associates Inc. Research and Computation Center Princeton N.J. United States Control and Information Systems Divisian School of Engineering Rensselaer Polytechnic Institute Troy N.Y. United States 

出 版 物：《IEEE Transactions on Automatic Control》 (IEEE Trans Autom Control)

年 卷 期：1968年第13卷第4期

页      面：400-407页

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0802[工学-机械工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Relays Control systems Asymptotic stability State-space methods Eigenvalues and eigenfunctions Vectors Information systems System performance Laplace equations 

摘      要：The global asymptotic stability of third-order relay control systems with real, nonpositive eigenvalues is related to conditions necessary for the existence of periodic solutions of such systems. By application of Popov s theorem it is shown that conditions which guarantee that a system will have no symmetric periodic solutions are also sufficient to insure the absolute stability of the origin. This result allows a relay system to be designed by choosing the switching function subject to the constraint that the switching plane avoid a certain easily defined region of state space. Copyright © 1968 by The Institute of Electrical and Electronics Engineers, Inc.