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In this paper, we address the problem of robust stability for uncertainsampled-data systems controlled by a discrete-time disturbance observer(DT-DOB). Unlike most of previous works that rely on the small-gain theorem,our approach is to investigate the location of the roots of the characteristicpolynomial when the sampling is performed sufficiently fast. This approachprovides a generalized framework for the stability analysis in the sense that(i) many popular discretization methods are taken into account; (ii) under fastsampling, the obtained robust stability condition is necessary and sufficientexcept in a degenerative case; and (iii) systems of arbitrary order and oflarge uncertainty can be dealt with. The relation between samplingzeros---discrete-time zeros that newly appear due to the sampling---and robuststability is highlighted, and it is explicitly revealed that the sampling zeroscan hamper stability of the overall system when the Q-filter and/or the nominalmodel are carelessly selected in discrete time. Finally, a design guideline forthe Q-filter and the nominal model in the discrete-time domain is proposed forrobust stabilization under the sampling against the arbitrarily large (butbounded) parametric uncertainty of the plant.

Robust Stability of Discrete-time Disturbance Observers: Understanding Interplay of Sampling, Model Uncertainty and Discrete-time Designs