A new polytopic approach for the unknown input functional observer design. Issue 3 (4th March 2018)

• Record Type: Journal Article
• Authors: Bezzaoucha, Souad; Voos, Holger; Darouach, Mohamed
• Is Part Of: International journal of control. Volume 91:Issue 3(2018)
• Page Start: 658
• Page End: 677
• Publication Date: 2018-03-04
• Subjects: Functional observers design -- nonlinear systems -- Takagi-Sugeno polytopic representation -- linear matrix inequality -- waste water treatment plant -- UAV control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2017.1288299
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: In this paper, a constructive procedure to design Functional Unknown Input Observers for nonlinear 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. Applying the Lyapunov theory and theL 2 attenuation, linear matrix inequalities conditions are deduced which are solved for feasibility to obtain the observer design matrices. To cope with the effect 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 sufficient 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. Both systems are highly nonlinear and represented in a T-S polytopic form with unmeasurable premise variables and unknown inputs.