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Stability Results of Popov‐Type for Infinite‐Dimensional Systems with Applications to Integral Control
Author(s) -
Curtain R. F.,
Logemann H.,
Staffans O.
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013916
Subject(s) - mathematics , control theory (sociology) , integrator , stability (learning theory) , bounded function , linearity , convergence (economics) , nonlinear system , interconnection , linear system , mathematical analysis , control (management) , computer science , engineering , artificial intelligence , machine learning , computer network , physics , bandwidth (computing) , quantum mechanics , economic growth , electrical engineering , economics
We derive absolute stability results of Popov‐type for infinite‐dimensional systems in an input‐output setting. Our results apply to feedback systems where the linear part is the series interconnection of an L 2 ‐stable linear system and an integrator, and the non‐linearity satisfies a sector condition which allows for non‐linearities with lower gain equal to zero (such as saturation, or more generally, bounded non‐linearities). These results are used to prove convergence and stability properties of low‐gain integral feedback control applied to L 2 ‐stable linear systems subject to actuator and sensor non‐linearities. The class of actuator/sensor non‐linearities under consideration contains standard non‐linearities which are important in control engineering such as saturation and deadzone. Moreover, we use the input‐output theory developed to derive state‐space results on absolute stability and low‐gain integral control for strongly stable well‐posed infinite‐dimensional linear systems. 2000 Mathematics Subject Classification 45M05, 45M10, 93B52, 93C10, 93C20, 93C25, 93D05, 93D09, 93D10, 93D25.