Simultaneous state and parameter estimation of a class of MIMO nonlinear systems

An adaptive nonlinear observer is conceived for simultaneous state and parameter estimation of a class of Multiple-Input-Multiple-Output(MIMO) nonlinear systems. Under the persistent excitation condition, it is shown that the overall observer injection gain, that ensures the convergence of the system states and the adaptive parameters, is composed by a sum of a constant and a time-varying gains. It is found that the constantgain output injection is sufficient to make the observer globally convergent under the condition that all the system parameters are known. In addition, if the persistent excitation condition is verified, the time-varying output injection is easily conceived by appropriate selection of a free design parameter. The observer design methodology is stated as the solution of a linear matrix inequality which is numerically tractable. Simulation results are shown to validate the theoretical results.