Klamka, J. Schauder’s fixed-point theorem in nonlinear controllability problems. (English) Zbl 1011.93001 Control Cybern. 29, No. 1, 153-165 (2000). The paper presents a review of results existing in the literature which show how Schauder’s fixed-point theorem can be practically used to solve several controllability problems for different types of nonlinear control systems in both finite- and infinite-dimensional spaces. The following nonlinear control systems are considered: finite-dimensional systems, systems with delays in control or in the state variables, and infinite-dimensional systems. Reviewer: S.K.Ntouyas (Ioannina) Cited in 2 ReviewsCited in 62 Documents MSC: 93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory 93B05 Controllability 47J05 Equations involving nonlinear operators (general) 47H10 Fixed-point theorems 93C10 Nonlinear systems in control theory 93C23 Control/observation systems governed by functional-differential equations 93C25 Control/observation systems in abstract spaces Keywords:controllability; nonlinear control systems; systems in abstract spaces; fixed-point theorems; delays PDFBibTeX XMLCite \textit{J. Klamka}, Control Cybern. 29, No. 1, 153--165 (2000; Zbl 1011.93001)