Damping feedback stabilization for time-dependent nonlinear control affine systems

This paper studies the stabilization of time-dependent affine nonlinear control systems by using time-dependent damping feedback control. A time-dependent auxiliary function is first construct using a homotopy operator. Providing that the obtained function is a weak Jurdjevic-Quinn function, the time-varying auxiliary function is used to construct a damping feedback controller. Stability of the closed-loop system is then shown using a Lyapunov function obtained by reshaping the auxiliary function. An application example is presented to illustrate the proposed construction.