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Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach
- Source :
- Mathematical Problems in Engineering, Vol 2019 (2019)
- Publication Year :
- 2019
- Publisher :
- Hindawi Limited, 2019.
-
Abstract
- This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.
- Subjects :
- 0209 industrial biotechnology
State variable
Article Subject
lcsh:Mathematics
General Mathematics
General Engineering
02 engineering and technology
Interval (mathematics)
Fuzzy control system
lcsh:QA1-939
Stability (probability)
Upper and lower bounds
Fuzzy logic
Stability conditions
020901 industrial engineering & automation
lcsh:TA1-2040
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
020201 artificial intelligence & image processing
lcsh:Engineering (General). Civil engineering (General)
Legendre polynomials
Mathematics
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2019
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....905cbbe4c857ce565c368847ca64bd21