Estimation of Order of Settling-time using Strict Lyapunov Function for Finite-time PD Control

This paper proposes a design method of an upper bound of the settling-time for the closed-loop system of the second-ordered system and the finite-time PD control. The proposed method provides the upper bound and its order with respect to P-gain and D-gain, where the order means that when the order is negative (resp. positive), the larger the gains, the faster (resp. slower) the convergence. Through analysis using the strict Lyapunov function, the proposed method provides a better order of the upper bound than the conventional one. In addition, we show a sufficient condition of the gains that achieve the negative order.