Unknown input functional observers design for polytopic discrete time systems

In this paper, a step by step algorithm is given to design functional unknown input observer for nonlinear discrete time systems under the Polytopic Takagi-Sugeno framework (also known as multiple models systems). Applying the Lyapunov theory and the ℒ2 attenuation, 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 solver based solution is proposed. The novelty of the proposed approach consists in solving simultaneously both structural constraints and LMIs, which ensure a mean for the efficient design of the gains of the observers. To illustrate the proposed theoretical results, an application example of model reference tracking control applied to an electro-mechanical model of a motor with a time varying parameter is discussed.