期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 23, 期 4, 页码 1314-1322出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2014.2347993
关键词
Path-following method; piecewise polynomial Lyapunov function (PPLF); polynomial fuzzy model; region-of-attraction (ROA); stability; sum-of-squares (SOS)
资金
- Grants-in-Aid for Scientific Research [25420215] Funding Source: KAKEN
This paper proposes sum-of-squares (SOS) methodologies for stability analysis and region-of-attraction (ROA) estimation for nonlinear systems represented by polynomial fuzzy models via piecewise polynomial Lyapunov functions (PPLFs). At first, two SOS-based global stability criteria are proposed by applying maximum-type and minimum-type PPLFs, respectively. It is known that less-conservative results can be obtained by reducing global stability to local stability, since it is usually the case for nonlinear systems that the stability cannot be reached globally. Therefore, based on the two types of PPLFs, two local stability criteria are further proposed with the algorithms that enlarge the estimated ROA as much as possible. The constraints for checking (global and local) stability and enlarging the estimated ROA are represented in terms of bilinear SOS problems. Hence, the path-following method is applied to solve the bilinear SOS problems in the proposed methodologies. Finally, some examples are provided to illustrate the utility of the proposed methodologies.
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