In this paper, the quadrotor stabilization under time and state constraints is studied. The objective is to design a nonlinear controller under time and state constraint for quadrotor. The nonlinear quadrotor model is built by the Euler-Lagrange approach while ignoring the Coriolis terms, hub moment and force. Based on quadrotor's dynamic model, a nonlinear feedback controller is designed for the quadrotor stabilization under time and state constraints. This feedback is an implicit PID controller where the feedback gains are obtained from LMIs (Linear matrix inequalities). LMI system characterizing the system stability and convergence properties is built based on convex embedding approach and implicit Lyapunov function method. To demonstrate the application prospects of implicit PID controller, robustness analysis is provided to show the property of implicit PID controller under external disturbance. The key novelty of this paper is that the implicit PID controller is proven feasible for applying to the quadrotor under time and state constraints, which is also the main outcome.