This paper deals with sampled-data control design for mechatronic systems represented by continuous-time Takagi-Sugeno (T-S) descriptors. This contribution is formulated in terms of a new relaxed LMI-based procedure obtained by a convenient choice of a non-quadratic Lyapunov-Krasovskii functional, the application of some useful lemmas, and quadratic polynomial constraints. From these conditions, it is possible to maximize the admissible sampling interval and estimate the closed-loop sampled-data domain of attraction. The effectiveness of this proposal is illustrated and benchmarked with previous literature results by considering the well-known underactuated mechatronic system of an inverted pendulum on a cart.