Some theoretical investigations of large angle attitude manoeuvres have been based on the application of Lyapunov's stability theory. With this method Mortensen derived stable control laws for performing attitude manoeuvres with either thrusters or reaction wheels. Previous results were idealized in that they ignored the nonlinearities inherent in the operation of both types of actuators. The present paper extends the scope of this work by acknowledging the actuator nonlinearities. The approach selected is to estimate the domain of attraction (DOA) of the target equilibrium for the system corresponding to the idealized control laws constrained by the actuator nonlinearities. The DOA is estimated by searching for the largest region of asymptotic stability over a set of quadratic Lyapunov functions. This approach results from the application of a theorem of Lasalle and gives rise to two nested nonlinear optimization problems, the internal one of which is a constrained global problem with several local minima. The paper gives an overview of the progress made in solving problems of this complexity. Emphasis has been placed on the parametrization of quadratic Lyapunov functions and a detailed comparison of several candidate nonlinear optimization techniques has been made for both the constrained and unconstrained optimization problem. Areas requiring further research are identified.
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