Pole Placement Theorem for Linear Measurable Time-Varying Control Systems with Single Input

The main object of this paper is linear time-varying control systems with single input. The coefficients of these systems are assumed only measurable and essentially bounded. We show that, for the dichotomy (Sacker–Sell) spectrum, uniform complete controllability is a necessary and sufficient condition, while for the Lyapunov spectrum, it is a sufficient condition for assignability by linear bounded state feedback. These achievements extend the results from [ 22 ] and [ 4 ] for systems with piecewise continuous and bounded coefficients to a wider class of control systems.