Curtain, R. F.; Logemann, H.; Staffans, O. Stability results of Popov-type for infinite-dimensional systems with applications to integral control. (English) Zbl 1032.93061 Proc. Lond. Math. Soc., III. Ser. 86, No. 3, 779-816 (2003). This paper considers feedback systems when the linear part contains an integrator (meaning in particular that the linear system is not input-output stable) and where at the same time the lower gain of the nonlinearity is allowed to be equal to 0 (which, for example, is the case for bounded nonlinearities such as a saturation). Absolute stability results are used to develop an input-output theory of low-gain integral control in the presence of input and output nonlinearities. Some applications to well-posed state-space systems are presented. Reviewer: M.Megan (Timişoara) Cited in 11 Documents MSC: 93D10 Popov-type stability of feedback systems 93C25 Control/observation systems in abstract spaces 93D25 Input-output approaches in control theory 45M05 Asymptotics of solutions to integral equations Keywords:absolute stability; Popov stability; infinite-dimensional systems; integral control; saturation; low-gain control; input nonlinearities PDFBibTeX XMLCite \textit{R. F. Curtain} et al., Proc. Lond. Math. Soc. (3) 86, No. 3, 779--816 (2003; Zbl 1032.93061) Full Text: DOI