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Nonfragile$\mathcal{H}_{\infty}$Control for Fuzzy Markovian Jump Systems Under Fast Sampling Singular Perturbation.
- Source :
-
IEEE Transactions on Systems, Man & Cybernetics. Systems . Dec2018, Vol. 48 Issue 12, p2058-2069. 12p. - Publication Year :
- 2018
-
Abstract
- This paper is concerned with the nonfragile ${\mathcal {H}_{\infty }}$ control problem for discrete-time fast sampling Markovian jump singularly perturbed nonlinear systems described by the Takagi-Sugeno fuzzy model. By utilizing singular perturbation theory, a singular perturbation parameter (SPP) independent, i.e., ${\epsilon }$ -independent, condition is derived to make sure the underlying closed-loop system’s stability and a mixed $ {\mathcal {H}_{\infty }}$ and passive performance ${\gamma }$ , simultaneously. The ill-conditioned case caused by SPP could be eliminated on the basis of such a condition. With the aid of the stochastic analysis approach, the desired controller gains can be obtained, where the nonfragile property is fully considered to improve the tolerance of controller. Furthermore, a technique is developed to estimate the upper bound of SPP $\boldsymbol {\epsilon }$ in this paper by employing a useful inequality. The availability and practicability of the proposed design method are finally explained via a practical example of a tunnel diode circuit with a modified model and a numerical example. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MARKOVIAN jump linear systems
*PERTURBATION theory
Subjects
Details
- Language :
- English
- ISSN :
- 21682216
- Volume :
- 48
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Systems, Man & Cybernetics. Systems
- Publication Type :
- Academic Journal
- Accession number :
- 133096158
- Full Text :
- https://doi.org/10.1109/TSMC.2017.2758381