Robust control of triangular tethered satellite formation with unmeasured velocities

This article researches the stable deployment of a triangular tethered satellite formation (TTSF) with velocities unmeasurable. By state space transformation, the system is transformed to four subsystems. Controllers with two kinds of robust terms are proposed and proved to make the system asymptotically stable. Then a high gain observer is given to estimate unmeasurable velocity variables in the system, where the design principles of the observer gains are found as well, and the system is locally asymptotically stable for the nonlinearities in the observer. Furthermore, the factors affecting the convergence of the system in the presence of state observer are found by virtue of Lyapunov function. Numerical simulation validates the effectiveness of the proposed controller and the stability of the system with state observer.