Robust observer design for a class of discrete‐time nonlinear singular systems with persistent disturbances

Abstract

SummaryThis article addresses the design of a nonlinear observer for nonlinear uncertain discrete‐time descriptor systems. The nonlinearities that appear in both state and output equations fulfill a Lipschitz‐like condition locally. Besides, the parametric uncertainties can affect the state dynamics as well as the input and output channels. The design methodology ensures input‐to‐state stability of the observer while minimizing an upper bound on a peak‐to‐peak performance index relating the disturbances/parametric uncertainties and the error in estimating a given performance signal. The observer design is cast as a convex optimization problem involving a set of linear matrix inequalities subject to a linear matrix equality constraint. The effectiveness of the proposed method is illustrated by numerical examples.