H∞ for quadrotor attitude stabilization

This paper proposes a state feedback controller for the attitude stabilization problem of quadrotors. The quadrotor attitude is represented by unit quaternion and disturbance of the attitude model is taken into consideration. A robust controller is synthesized via H
_∞
optimal design approach. Solving the nonlinear H
_∞
optimal control problem using state feedback is meltdown to finding a solution to a Hamilton-Jacobi inequality. Based on the quadrotor attitude dynamics, an appropriate parameterized Lyapunov function is selected and the corresponding state feedback controller is derived. Then the parameters are found from a Hamilton-Jacobi inequality. The resultant state feedback controller can lead to closed-loop nonlinear system having L
₂
-gain less than or equal to a constant γ, and establish the asymptotically stability of the closed-loop nonlinear system without external disturbance. The simulation provides the results to show the stability and the robust performance against to disturbance.