A New Polytopic Approach for the Unknown Input Functional Observer Design

In this paper, a constructive procedure to design Functional Unknown Input Observers for nonlin
ear continuous time systems is proposed under the Polytopic Takagi-Sugeno framework. An equivalent representation for the nonlinear model is achieved using the Sector Nonlinearity Transformation (SNT).
Applying the Lyapunov theory and the L2 attenuation, Linear Matrix Inequalities (LMI)s conditions are deduced which are solved for feasibility to obtain the observer design matrices. To cope with the e ffect of unknown inputs, classical approach of decoupling the unknown input for the linear case is used. Both algebraic and solver based solutions are proposed (relaxed conditions). Necessary and su fficient conditions for the existence of the functional polytopic observer are given. For both approaches, the general and particular cases (measurable premise variables, full state estimation with full and reduced order cases) are considered and it is shown that the proposed conditions correspond to the one presented for standard linear case.
To illustrate the proposed theoretical results, detailed numerical simulations are presented for a Quadrotor Aerial Robots Landing and a Waste Water Treatment Plant (WWTP). Both systems are highly nonlinear and represented in a T-S polytopic form with unmeasurable premise variables and unknown inputs.