Simple But Useful Contributions to High-Gain Observer for Non-Triangular Systems

This letter deals with nonlinear observer design for a class of non-triangular systems satisfying the sector condition. Under such a sector condition on the nonlinearity of the system, simple but useful contributions to the design of high-gain observers are proposed for systems with arbitrary nonlinear structures contrary to the standard results on high-gain observer methodology developed for triangular nonlinearities. First, based on the use of a convenient decomposition of the nonlinear function, a general design method is provided. Compared to the standard high-gain observer, the proposed method requires an extra constraint on the tuning parameter to dominate the non-triangular components of the nonlinearity of the system. To reduce the conservatism of the extra-condition, further results are established by exploiting the Linear Matrix Inequality (LMI) based approach. A numerical design algorithm is provided to build all the observer parameters. Finally, an illustrative example is presented to show the effectiveness and validity of the proposed technique.