Abstract
The well known Takagi–Sugeno (T–S) fuzzy model can be extended in different ways including the polynomial fuzzy model, whose consequent parts are polynomial sub-systems. Compared with the traditional T–S fuzzy model, the polynomial fuzzy model can represent a nonlinear system more accurately with a smaller number of fuzzy logic rules. It is worth emphasizing that the stability analysis and controller design of polynomial fuzzy model-based (PFMB) control systems are not based on the linear matrix inequalities but the recently developed sum-of-squares decompositions. In this paper, based on an existing result for traditional fuzzy control systems, we propose a new stability condition for the stability analysis of PFMB control systems. Furthermore, the stability of PFMB control systems with parameter uncertainties is investigated. The popular inverted pendulum and an unstable nonlinear system are employed to demonstrate the quality of the proposed stability conditions.
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Acknowledgments
This research work was funded by the NSFC under Grant No. 60874084. X. Z. Gao’s work was also funded by the Academy of Finland under Grants 135225 and 127299. The authors would like to thank Dr. H. K. Lam of King’s College London and the anonymous referees for their constructive comments and suggestions.
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Communicated by A. Di Nola.
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Cao, K., Gao, X.Z., Vasilakos, T. et al. Analysis of stability and robust stability of polynomial fuzzy model-based control systems using a sum-of-squares approach. Soft Comput 18, 433–442 (2014). https://doi.org/10.1007/s00500-013-1066-y
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DOI: https://doi.org/10.1007/s00500-013-1066-y