Analytical solutions to the matrix inequalities in the robust control scheme based on implicit Lyapunov function for spacecraft rendezvous on elliptical orbit

In this study, the problem of robust control for spacecraft rendezvous on elliptical orbit, which contains parameter uncertainties and external disturbances, is investigated based on the implicit Lyapunov function method. A state-feedback controller is first designed, and its existence conditions are derived in terms of linear matrix inequalities (LMIs) which should be solved in real time. An analytical solution to these LMIs is provided to greatly reduce the computational burden. On the basis of the state-feedback analysis, an observer-based output-feedback controller is proposed, and it is proved finite-time stable by constructing an analytical solution to the parameterised nonlinear matrix inequalities (NLMIs). The advantage brought by the proposed analytical solution is that whether these NLMIs hold only need to be checked at two points, while in previous researches they were supposed to be checked at infinite points. The effectiveness of the theoretical results is illustrated by simulation examples.