Quasi Input-to-State Stability of a Quaternion-based Attitude Control System with an Augmented Dynamical System

Quaternion-based attitude control system design and analysis is challenging due to fact that a physical attitude is represented by two points in a quaternion. It then implies the existence of two equilibrium points. If the attitude control system is not designed properly, it would perform undesired behavior called unwinding phenomenon. A quaternion-based continuous attitude controller with an augmented dynamical system that plays a role in making the system able to stabilized two equilibrium points from all possible initial conditions while avoiding unwinding phenomenon has been reported. However, it was designed without considering the existence of disturbance torque which is effectively applied in the real situation. This paper studies stability analysis based on quasi input-to-state stability for the attitude control system. Characteristics of the quasi input-to-state Lyapunov function are investigated. Simulations carried out show the effectiveness of the designed attitude control system based on the quasi input-to-state stability guarantee.