“The final publication is available at Springer via http://dx.doi.org/10.1007/s10852-012-9212-6"In this paper a class of linear time-varying control systems is considered. The time variation consists of a scalar time-varying coefficient multiplying the state matrix of an otherwise time-invariant system. Under very weak assumptions of this coefficient, we show that the controllability can be assessed by an algebraic rank condition, Kalman canonical decomposition is possible, and we give a method for designing a linear state-feedback controller and Luenberger observer
