Observer design for discrete nonlinear descriptor systems

A nonlinear observer is considered for a class of discrete nonlinear descriptor systems subject to unknown inputs. This class is partly characterised by globally Lipschitz nonlinearities and a member system may be singular. First, the system is transformed into SVD-form from which a preliminary feedback control function can be designed, if needed, to render the system causal. Then a nonlinear observer is proposed which is based on the solution of a Riccati equation and on the use of a quadratic Lyapunov function. A design algorithm is given and applied to the estimation of the states of a flexible joint robot.