Observers with impulsive dynamical behavior for linear and nonlinear continuous-time systems

This paper presents new observers for Lipschitz nonlinear systems, for systems with nondecreasing nonlinearities, and for linear systems. The dynamics of these observers exhibits impulsive dynamical behavior due to the update of the observer state at discrete instants of time. Conditions are given to ensure global convergence of these observers and possible applications are discussed. Furthermore, several approaches are proposed to design the observer matrices via linear matrix inequality (LMI) techniques. Finally, the proposed impulsive observer for Lipschitz nonlinear systems is applied to estimate the system state of a flexible joint robotic arm.