Robust H∞ observers for Lipschitz nonlinear discrete-time systems with time delay

Issues of observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay and disturbance input are addressed, where the Lipschitz condition is expressed in a componentwise rather than aggregated manner. It has been shown that both full-order and reduced-order robust H. observers can be obtained by means of the same convex optimisation procedure with minimisation of the disturbance attenuation upper bound gamma > 0. It is also shown that for a prescribed H-proportional to-norm upper bound y > 0, the tolerable Lipschitz bounds can be obtained by another convex optimisation procedure. A numerical example is presented to show the effectiveness of the developed approach.