High-gain observer for a class of time-delay nonlinear systems

This paper proposes a high gain observer design for a class of nonlinear systems with multiple known time-varying delays intervening in the states and the inputs. In the free delay case, the class of systems under consideration coincides with a canonical form characterizing a class of multi outputs nonlinear systems which are observable for any input. The underlying high gain design has been mainly motivated by its inherent simplicity from both design and implemen-tation points of view. Indeed, the observer gain is determined from an explicit resolution of a time-invariant Lyapunov algebraic equation up to the specification of a single design parameter. An academic observation problem is addressed to illustrate the effectiveness of the proposed observer.