A SYSTEMATIC-APPROACH TO ADAPTIVE-OBSERVER SYNTHESIS FOR NONLINEAR-SYSTEMS

Geometric techniques of controller design for nonlinear systems have e njoyed great success. A serious shortcoming, however, has been the nee d for access to full-state feedback, This paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty. An adaptive nonlinear observer is suggested for Lipschitz nonlinear systems, and the stability of this observer is sh own to be related to finding solutions to a quadratic inequality invol ving two variables, A coordinate transformation is used to reformulate this inequality as a linear matrix inequality. A systematic algorithm is presented, which checks for feasibility of a solution to the quadr atic inequality and yields an observer whenever the solution is feasib le, The state estimation errors then are guaranteed to converge to zer o asymptotically. The convergence of the parameters, however, is deter mined by a persistence-of-excitation-type constraint.