This paper describes the design of a nonlinear controller for a coaxial tricopter, which is designed and calculated using Lyapunov stability theory and a linear matrix inequality (LMI). This controller is robust to reject parametric perturbations and uncertainties and is formulated from a linear approximation around multiple equilibrium points, which allows the system to work at different points of operation. This is a novel technique for the design of controllers for the coaxial tricopter when its behavior is described by a mathematical model derived from the Euler-Lagrange formalism. The controller is tested by simulation in Simulink of MATLAB, results show a performance in accordance with the design requirements.