The aim of this paper is to present the synthesis of a robust control law for the control of a class of nonlinear systems named Liouvillian. The control design is based on a sliding-mode uncertainty estimator developed under the framework of algebraic-differential concepts. The estimation convergence is done by the Lyapunov-type analysis and the closed-loop system stability is shown by means of the regulation error dynamics. Robustness of the proposed control scheme is tested in the face of noise output measurements and model uncertainties. The performance of the proposed control law is illustrated with numerical simulations in which a class of oscillatory chemical system is used as application example.
Two different nonlinear observers are employed in the fault diagnosis problem of nonlinear systems. A system with two types of faults (multiplicatives and additives) is analized and both faults are estimated with each observer. Some numerical results are shown to ilustrate this methodology and finally, some concluding remarks are given.
A g r a d e c i m i e n t o sDeseo agradecer profúndamente a 10s Doctores Jesús De Ledn Morales y Javé Alvarez Ramirez, por SU apoyo constante y por la oportunidad que me brindaron para poder c o l a b o r a r con ellos, a s í como, por haber aceptado formar parte d e l Jurado. Mi agradecimiento muy especial a mi asesor. el Dr. Rudol/o Suúrez Cortes, por su invaluable apoyo y su valioso asesoramiento que hizo posible concluir el presente trabajo. Mi agradecimiento al Dr. Selle Diop, que two la gentileza de invitarme al Laboratoire de Signaux et systemes d e l CNRS, Gif s/yvette Francia y dedicó su tiempo para la revisión y discusión d e l presente trabajo y el haber aceptado formar parte del J u d o .Finalmente, quiero agradecer a mi esposa Marilh y a mi hijo Rafael su amor, comprensión y su apoyo en todo momento; así también extiendo este agradecimiento a mis padres C a r h y Virginia, a s í como, a mi hermanos Javier, Victor, Arluro y Marisela.
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