Abstract
This study is concerned with the properties of absolute stability independent of the delays of time-delay systems, possessing non commensurate internal point delays, for any nonlinearity satisfying a Popov’s- type time positivity inequality. That property holds if an associate delay-free system is absolutely stable and the size of the delayed dynamics is sufficiently small. The results are obtained for nonlinearities belonging to sectors [0, k] and [h, k+h], and are based on a parabola test type.
Highlights
The absolute stability of dynamic is an interesting issue since it refers to the global asymptotic stability of a system under any feedback law provided by a wide class of nonlinear devices
The problem has been widely studied for the plant delay-free case and nonlinear feedback devices within linear sectors [k1, K2] and (k1, K2) in (0, ∞) [1,2,3,4,5,6]
Re s < 0) provided that its H ∞ -by is upper-bounded with a sufficiently small upper-bound and that the feedback nonlinear device satisfies certain local Liptschitzian [regularity conditions[7] and to systems with external delays[8]. In this study, such assumptions are removed by allowing nonlinearities satisfying a sector-type positivity constraints, multiple non commensurate internal delays and either strictly stable or critically stable linear plants with a single critically stable pole at s=0
Summary
The absolute stability of dynamic is an interesting issue since it refers to the global asymptotic stability of a system under any feedback law provided by a wide class of nonlinear devices. Some of those results have been extended to single- delay cases provided that the transfer function of the linear subsystem is (non critically) stable
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
