In engineering practice delay-difference is often used to approximate the derivatives of output signals for feedback control, which leads to a closed-loop system with delay both in the states and in the system coefficients. Our objective is to find all the delay values below some upper bound that guarantee the exponential stability of the closed-loop system subject to the delay-difference approximation. A method for stability analysis of systems with delay-dependent coefficients developed in our previous work is extended and applied for the systems considered in this paper. The proposed stability analysis procedure is demonstrated through the design of a mobile-robot path-following controller.