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The paper presents a rigorous perturbation analysis of the QR decomposition A = Q R of an n × m matrix A using the method of splitting operators. New asymptotic componentwise perturbation bounds are derived for the elements of Q and R and the subspaces spanned by the first p ≤ m columns of A. The new bounds are less conservative than the known bounds and are significantly better than the normwise bounds. An iterative scheme is proposed to determine global componentwise bounds in the case of perturbations for which such bounds are valid. Several numerical results are given that illustrate the analysis and the quality of the bounds obtained. [ABSTRACT FROM AUTHOR]

This study deals with the problem of state bounding for positive singular discrete‐time systems with time‐varying delay and bounded disturbances. First, the authors derive some new conditions for the existence of componentwise bounds of the state vector of the systems without disturbances. Then, in the case of systems with bounded disturbances, they obtain a sufficient condition for the existence of componentwise ultimate bounds. Since the conditions are given in terms of the spectral radius of the system matrices, they can check them easily and compute directly the smallest componentwise ultimate bound. In addition, the problem of state bounding for positive time‐varying singular systems is also investigated in this study. Finally, numerical examples are provided to illustrate the effectiveness and advantages of their results. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]