Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances

In this paper, we study the robust observer design and observer-based control design problems for a class of discrete one-sided Lipschitz systems subject to uncertainties and disturbances. The nonlinearities are assumed to be one-sided Lipschitz and quadratically inner-bounded. By utilizing a new approach which is an extension of the H ∞ filtering method, our robust observer design can relax some limitations in existing works. In order to derive design conditions in terms of linear matrix inequalities, several mathematical techniques are appropriately used to linearize the bilinear terms which unavoidably emerge in observer and observer-based control designs for discrete-time uncertain systems. Via a numerical example, we show that while existing works fail, our results work effectively.