A Polytopic Observer Design Approach for Landing Control of a Quadrotor UAV

Abstract

In this paper, a constructive procedure to design functional unknown input observer for nonlinear continuous time systems under the Polytopic Takagi-Sugeno framework (also known as multiple models systems) is proposed. Applying the Lyapunov theory, Linear Matrix Inequalities (LMI)s conditions are deduced which are solved for feasibility to obtain observer design matrices. To reject the effect of unknown input, classical approach of decoupling the unknown input for the linear case is used. A comparative study between single and Polytopic Lyapunov function is made in order to prove the relaxation effect of the Multiple functions. A solver based solution is then proposed.It will be shown through applicative example (a Quadrotor Aerial Robots Landing) that even if the proposed LMIs solver based solution may look conservative, an adequate choice of the solver makes it suitable for the application of the proposed approach.