Stabilization of linear time

This paper presents the stabilization approach for linear time-varying continuous-time systems using proportional-derivative (PD) state feedback control. The solvability conditions for the problem are considered. The general analytical expressions for the PD controller gains are derived, which describe the available degrees of freedom offered by PD state feedback. The non-uniqueness of the controller gains is utilized to obtain closed-loop systems with small gain elements. Two numerical examples are introduced to demonstrate the effectiveness of the proposed approach