Learning machine for polytopic nonlinear observer design

The design of nonlinear systems observer with global convergence when nonlinearities are not available in real time is proposed. A support vector machine is chosen in order to estimate the nonlinearities from the only available information, that is the output of the system, in a unified framework for both piecewise linear systems or nonlinear systems. The global convergence of the observer is ensured by a polytopic decomposition of the system state representation which enables one to compute the gain of the observer by solving a set of linear matrix inequalities derived from recent results of poly-quadratic stability. The proposed design attempts to enlarge the class of nonlinear systems for which an observer can be synthesized.