Controller design for asymptotic stability of flexible spacecraft

Using invariance principle several linear and nonlinear state variable feedback control laws for ensuring global asymptotic stability (g.a.s.) of the equilibrium state of a large flexible spacecraft are derived. The Hamiltonian of the system is used as an appropriate Lyapunov function for deriving stabilizing control laws. Necessary and sufficient conditions for the existence of stabilizing controller are presented. It is shown that stabilizing control law exists if and only if certain observability condition is satisfied. Using modal decomposition, a simple test for control laws ensuring g.a.s. based on simplified observability condition is devised. For illustration, application to a specific spacecraft model is presented.