Extensions to “Stability Analysis of Fuzzy Control Systems Subject to Uncertain Grades of Membership”

Abstract

In the December 2005 issue of this journal, Lam and Leung proposed stability results for fuzzy control systems where the membership functions in the controller were not the same as those from the process one, but some multiplicative bounds were known. The main practical context where that situation arises is the uncertain knowledge of the memberships of a Takagi-Sugeno model. This correspondence presents further extensions of those results, allowing for a richer description of the membership uncertainty, in terms of affine inequalities.

Asynchronous Piecewise Output-Feedback Control for Large-Scale Fuzzy Systems via Distributed Event-Triggering Schemes

“…In particular, the premise variables of the distributed piecewise controller in (12) undergo event-triggering control, such that the asynchronous premise variable spaces between ζ i (t) andζ i (t) are closer to the actuals. It has been shown in [31], when the information between ζ i (t) andζ i (t) is unavailable, this condition tends to generate a linear controller, which lowers the stabilization ability of the desired controller.…”

“…When requiring priori asynchronous knowledge, the work in [30] derived the LMI-based design results on fuzzy controller. In [31], further extensions to uncertain grades of membership were presented, and the less conservative results were derived by relaxing some restrictive conditions. In [32], the asynchronous grades of membership were considered as disturbances, and the design of fuzzy statefeedback controller to synchronize the chaotic systems was derived in the form of LMIs.…”

Fuzzy control turns 50: 10 years later

“…A more focused approach to type-2 control, as a way to analyse uncertain nonlinear systems, might be interval approaches pursued in, for instance, [121]. However, the underlying idea is, philosophically, related to older literature in which "imperfect knowledge of the plant memberships" is assumed, such as [122].…”

Relaxed stability conditions based on Taylor series membership functions for polynomial fuzzy-model-based control systems

“…The polynomial fuzzy model and controller in this paper do not share the same membership functions, meaning non-PDC design is employed which improves the design flexibility and reduces the complexity of the controller [34].…”