Abstract
Different from the other work, the almost sure asymptotic stability of an uncertain stochastic T–S fuzzy system driven by Lévy noise has been investigated. However, the Lévy noise caused the càdlàg paths in the system, and the uncertainty was the linear fractional form, which made difference to the general norm-bounded type. Using the special stochastic techniques and new matrix decomposition method, we deal with the càdlàg paths and uncertainty of the system. As the main results, the sufficient conditions of almost sure asymptotic stability for stochastic T–S fuzzy system driven by Lévy noise have been presented. On this basis, the closed-loop system is robustly almost surely asymptotically stable with fuzzy state-feedback controller. Furthermore, our stabilization criteria are based on linear matrix inequalities (LMIs), whence the feedback controller could be designed more easily in practice.
Highlights
With the improvement of linear system theory, the research of nonlinear system has become a difficult problem
Based on the above discussion, this paper considers the problems of almost sure asymptotic stability analysis and controller synthesis for a class of uncertain stochastic T–S fuzzy systems driven by a multi-dimensional Lévy process
6 Discussion of the main results The paper has considered the almost sure asymptotic stability of an uncertain stochastic T–S fuzzy system driven by Lévy noise
Summary
With the improvement of linear system theory, the research of nonlinear system has become a difficult problem. Based on the above discussion, this paper considers the problems of almost sure asymptotic stability analysis and controller synthesis for a class of uncertain stochastic T–S fuzzy systems driven by a multi-dimensional Lévy process. Following the same idea as in dealing with the stabilization problem, linear state feedback controllers are designed so that the closed-loop systems are almost surely asymptotically stable.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
