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Stability analysis for discrete‐time fuzzy system by utilizing homogeneous polynomial matrix function |
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| Authors: | Likui Wang Xiaodong Liu |
| Affiliation: | 1. School of Electronic and Information Engineering, Dalian University of Technology;2. School of Mathematics and Information Science, Nanchang Hangkong University;3. School of Electronic and Information Engineering, Dalian University of Technology, 2 Linggong Road, Dalian, 116024, China |
| Abstract: | The purpose of this paper is to investigate the stability of nonlinear systems represented by a Takagi‐Sugeno discrete‐time fuzzy model. The homogeneous polynomial matrix function (HPMF) is developed to obtain new stabilization conditions. Applying the HPMF to the non‐parallel distributed compensation (non‐PDC) law and non‐quadratic Lyapunov function, some new stabilization conditions are obtained by the following two means: (a) utilizing the popular idea of introducing additional variables for some fixed degree of the HPMF; and (b) increasing the degree of the HPMF. It is shown that the conditions obtained with approach (a) are less conservative than some sufficient stability conditions available in the literature to date. It is also shown that as the degree of HPMF increases the conditions obtained under (b) become less conservative. An example is provided to illustrate how the proposed approaches compare with other techniques available in the literature. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society |
| Keywords: | Takagi– Sugeno's fuzzy model homogeneous polynomial matrix function non‐quadratic Lyapunov function parallel distributed compensation law linear matrix inequality |