Robust H∞ observer design for a class of Lipschitz discrete-time systems

We discuss the observer design for a class of Lipschitz nonlinear discrete-time systems with disturbance input, where the Lipschitz condition is expressed in a component-wise rather than aggregated manner. It is shown that both full-order and reduced-order robust H_∞ observers can be obtained by using the same convex optimization procedure with minimization of the disturbance attenuation upper bound γ > 0. It is also shown that for a prescribed H_∞-norm upper-bound γ > 0, the tolerable Lipschitz bounds can be obtained by another convex optimization procedure. Finally, an illustrative numerical example is presented to show the effectiveness of the developed approach.