Abstract
This paper presents a new interval Pade approximation method to convert a continuous-time (discrete-time) uncertain linear system to an equivalent discrete-time (continuous-time) uncertain model via interval arithmetic operations. Based on the inclusion theorem related to the interval arithmetic, the interval Pade's approximants and their associated interval error matrices with interval arguments are obtained via the Pade's approximants and their associated error matrices with degenerate (real) arguments, respectively. Tighter error bounds of various approximate uncertain models with respect to their exact uncertain models are determined and used to modify the obtained Pade's approximants, so that the resulting approximate uncertain models are able to tightly enclose the original uncertain systems. Thus, the analysis and design of the original uncertain systems can be indirectly carried out using the converted uncertain models in either the continuous-time or the discrete-time domain.
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This work was supported in part by the U.S. Army Research Office under contract DAAH-04-94-G-0227 and the NASA-Johnson Space Center under Grant NAG-9-746.
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Shieh, L.S., Gu, J. & Tsai, J.S.H. Model conversions of uncertain linear systems via the interval Pade approximation method. Circuits Systems and Signal Process 15, 1–22 (1996). https://doi.org/10.1007/BF01187691
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DOI: https://doi.org/10.1007/BF01187691