Observer design for nonlinear systems described by differential-algebraic equations

摘要

We propose an observer design method for a differential-algebraic equation (DAE) systems with index one. In the observer, the algebraic equation constraint is fulfilled asymptotically. The error of the constraint converges to zero in finite time by means of functions that do not satisfy the local Lipschitz condition. The dynamics part of the observer is designed via the linear matrix inequality (LMI) technique. The observer is globally asymptotically stable under certain assumptions. Since the algebraic equations include input variable, the observer requires the derivative of input to plant. The derivative of the input is calculated from the controller states directly or estimated by the exact differentiator of Levant.