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- Title
Padé-like approximation and its application in domain of attraction estimation.
- Authors
Yaghmaei, Abolfazl; Yazdanpanah, Mohammad Javad
- Abstract
In this paper, a rational approximation of multivariable functions is proposed. Since the proposed approach, hereafter called Padé-like approximation, uses the coefficients of Taylor series expansion at a point, it can be considered as a novel extension of conventional Padé approximation for multivariable functions. This extension is free from some of previous extensions imperfections. Similar to the conventional Pad'e approximation for one-variable functions, the outcome of the proposed method can reveal the points where the multi-variable function is non-analytic. The proposed method, whose accuracy is analytically guaranteed, could find a wide range of applications wherever an accurate approximation is needed. In the line of estimating domain of attraction in non-linear systems, Padé-like approximation of an optimal Lyapunov function (OLF) is obtained from the corresponding partial differential equation. Using the approximate OLF, an estimation of domain of attraction is obtained which is less conservative compared to those based on the previous techniques.
- Subjects
PADE approximant; LYAPUNOV functions; MULTIVARIABLE control systems; TAYLOR'S series; PARTIAL differential equations
- Publication
IMA Journal of Mathematical Control & Information, 2018, Vol 35, Issue 2, p661
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnw071