Synthesis of a Robust Multiobserver for the Estimation of Unknown Inputs Using the Piecewise Quadratic Functions | Science Publications

American Journal of Applied Sciences

Mongi Besbes¹  Elyes Maherzi¹  Radhi Mhiri¹  Sami Zemmel¹ 

关键词: Discrete multimodel;    unknown input multiobserver;    quadratic stabilization;    piecewise quadratic functions;    unknown input estimation;   

DOI  :  10.3844/ajassp.2010.1264.1276

学科分类：自然科学（综合）

来源: Science Publications

【 摘 要 】

Problem statement: The estimation of states and the unknown inputs of a nonlinearsystem described by a multimodel are done by a multiobserver. The stabilization of themultiobserver calls upon uses both quadratic and no quadratic functions of Lyapunov. Althoughthe stabilization using the quadratic approach is interesting from the point of view implementation,the step showed its limits for the multimodel. However, the problem paused by the quadraticmethod lies in the obligation to satisfy several LMI with respect to the same Lyapunov matrix P,these results are shown very conservative. Approach: To reduce the conservatism of the quadraticapproach we propose another approach which is exclusively based on Lyapunov piecewisequadratic functions. The conditions obtained by the stabilization of the multiobserver areexpressed in term of matrix inequalities with constraints on the matrices rank. Results: Theestimation of both states and unknown inputs of a multimodel using the quadratic approach perpieces leads to results less conservative than the quadratic approach. Academic examples illustratethe robustness of the piecewise quadratic approach. Conclusion: In this article we proposed newsufficient conditions of stability of a multiobserver able to the estimation of states and unknowninputs of a nonlinear system describes by a multimodel subjected to the influence of the unknowninputs. The study in was carried out by considering two approaches. The first approach is based onLyapunov quadratic functions; it is significant to note the great difficulty in finding satisfyingresults by this approach for the multimodel systems. For this reason we proposed an approachbased on piecewise quadratic functions which led to interesting results (proposition 1) and lessconservative than the quadratic approach. The conditions suggested in this article concern both themultiobserver stabilization and the estimation of states and the unknown inputs of a multimodelwith measurable variables of decision (??(k)). The synthesis of a multiobserver with nomeasurable variables of decision is not approached. This point can constitute an interestingprospect for this study.

【 授权许可】

Unknown