Controllability of state-linear dynamic systems (Q1882025)

Linear, finite-dimensional, continuous-time control systems with coefficients depending on the constrained controls are considered. Basic definitions of controllability are recalled and discussed. Using algebraic methods and certain decomposition into a projective and a radial subsystem, a sufficient condition for constrained global controllability in finite time is formulated and proved. A simple example which illustrates the theoretical considerations is also presented. Moreover, many remarks and comments on the controllability problem for continuous-time systems described by ordinary differential state equations are given. Finally, it should be pointed out that similar controllability problem have been considered in the monograph [\textit{J.Klamka}, Controllability of dynamical systems. Dordrecht: Kluwer (1991; Zbl 0732.93008)].