Systematic ultimate bound computation for sampled-data systems with quantization

We present a novel systematic method to obtain componentwise ultimate bounds in perturbed sampled-data systems, especially when the perturbations arise due to quantization. The proposed method exploits the system geometry as well as the perturbation structure, and takes intersample behavior into account. The main features of the method are its systematic nature, whereby it can be readily computer coded, without requiring adjustment of parameters for its application, and its suitability for dealing with highly structured perturbation schemes, whereby the information on the perturbation structure is directly taken into account. The latter feature distinguishes the method from other approaches that require a bound on the norm of the perturbation and thus disregard information on the perturbation structure. We apply the method to a numerical example taken from the literature to illustrate its simplicity and potential.