Observer synthesis for a class of MIMO non triangular nonlinear systems

A high gain observer is proposed for a class of nonlinear systems involving some uncertainties. In the absence of the uncertainties, the considered class of systems becomes a canonical form that characterizes a class of uniformly observable systems and the observation error exponentially converges to zero. In the presence of uncertainties, it is shown that the observation error can be made as small as desired by appropriately specifying the design parameter of the observer gain. Two main contributions are worth to be emphasized: the first one is related to the structure of the considered class of systems which does not assume a complete triangular structure. That is, each block may contain nonlinearities which depend on the whole state. The second one lies in the simplicity of the observer gain design since its calibration is reduced to the choice of a single design parameter. More specifically, it involves a design function that has to satisfy a mild condition which is given. Different expressions of such a function are proposed. Of particular interest, it is shown that high gain observers and sliding mode like observers can be derived by considering particular expressions of the design function. An example with simulation results is given for illustration purposes.