In order to achieve improved tracking performance, this paper considers the distinct features of tailless flapping wing micro air vehicles (FWMAVs), and proposes a robust $\bm{H_{\infty}}$ controller. A linear parameter Varying (LPV) model is established for a tailless FWMAV with parameter uncertainty, based on the complete dynamic and kinetic model with quasi-steady and linear damping. Sampled data is used as feedback signals in controller design to overcome the influence of the control period not being much larger than the flapping period. An input delay technique is employed to convert the sampled-data system into a continuous-time system with a state delay. The controller is restricted to a designed multivariable proportional-integral (PI) structure for practical engineering implementation. A Lyapunov-Krasovskii function is employed to establish the stability and $\bm{H_{\infty}}$  performance of the closed-loop,  and an optimization problem involving linear matrix inequalities (LMIs) is obtained using diagonal Lyapunov matrix hypotheses. Numerical simulations demonstrate the strong robustness of the proposed controller, and flight experiments verify its effectiveness and superior performance compared to a state-of-the-art benchmark controller.