Title :
Off-axis multivariable circle stability criterion
Author :
Harris, C.J. ; Husband, R.K.
Author_Institution :
Royal Military College of Science, Department of Electrical & Electronic Engineering, Swindon, UK
fDate :
9/1/1981 12:00:00 AM
Abstract :
In 1968, the scalar circle stability criterion was extended by Cho and Narendra to the off-axis case by the use of multipliers Q, Q¿1 which have an RL or RC realise structure, so that the product of the linear portion of the feedback system and the multiplier was positive-real. Fabl, Freedman and Zames produced a multivariable on-axis circle criterion for systems whose linear part is normal for all frequencies. As yet the off-axis circle criterion has not yet been established for the multivariable case, although Cook (1976) has shown that a criterion of this type does provide the conditions for the absence of limit cycles. Utilising the loop transformation theorem and the passivity theorem, an off-axis multivariable circle stability criterion is established via the method of multipliers for nonlinear feedback systems with a normal linear operator. The criterion is shown to have a simple graphical interpretation based on the Nyquist plots of the eigenvalues of the system.
Keywords :
eigenvalues and eigenfunctions; multivariable control systems; nonlinear control systems; stability criteria; Nyquist plots; eigenvalues; loop transformation theorem; multipliers method; nonlinear feedback systems; normal linear operator; off-axis multivariable circle stability criterion; passivity theorem;
Journal_Title :
Control Theory and Applications, IEE Proceedings D
Conference_Location :
9/1/1981 12:00:00 AM
DOI :
10.1049/ip-d:19810046