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Output linear controller for a class of nonlinear systems using the invariant ellipsoid technique

This paper deals with the problem of robust stabilization of an uncertain nonlinear system with output measurements using the invariant ellipsoid method. The non-linear system is uncertain but bounded according to a ‘quasi-lipschitz’ condition and the output measurements are subjected to perturbations bounded by ellipsoids.The invariant ellipsoid method allows to obtain the robust linear feedback as a solution of the special linear optimization problem with bilinear constraints. The methods for solving this optimization problem involves the LMI technique. The stabilization of the double mass-spring system is considered as an illustrative example.