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A Fuzzy Lyapunov Function Approach to Positive Ll Observer Design for Positive Fuzzy Semi-Markovian Switching Systems With Its Application.
- Source :
-
IEEE Transactions on Systems, Man & Cybernetics. Systems . Feb2021, Vol. 51 Issue 2, p775-785. 11p. - Publication Year :
- 2021
-
Abstract
- This paper concerns a positive $\mathcal {L}_{1}$ observer for positive nonlinear semi-Markovian switching systems (MSSs) via the expansion of Taylor formula and the fuzzy Lyapunov function approach, in which semi-Markovian switching parameters, positivity, Takagi–Sugeno (T–S) fuzzy, and external disturbance are all considered in a unified framework. A fuzzy Lyapunov function approach with less conservativeness is introduced into the research of positive systems. In the system under consideration, positive S-MSSs with the semi-Markovian process can describe more complex systems in a practical control process. The main motivation of this paper is that the practical system subject to positivity and abrupt changes can be described by positive nonlinear S-MSSs, which always needs to consider the external disturbance. First, by using the normalized membership function approach, positive nonlinear S-MSSs can be represented by local positive T–S fuzzy S-MSSs. Second, by constructing the fuzzy Lyapunov function, some sufficient conditions are proposed for stochastic stability and $\mathcal {L}_{1}$ -gain performance analysis, respectively. Then, a positive $\mathcal {L}_{1}$ observer in a novel standard linear programming condition is designed to guarantee the resulting closed–loop augmented system is positive and stochastically stable with a required $\mathcal {L}_{1}$ -gain performance. Finally, a practical example about the epidemiological model is introduced to show the effectiveness of the main theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 21682216
- Volume :
- 51
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Systems, Man & Cybernetics. Systems
- Publication Type :
- Academic Journal
- Accession number :
- 148208181
- Full Text :
- https://doi.org/10.1109/TSMC.2018.2882536