Guaranteed Set-Membership Estimation for Local Nonlinear Uncertain Fuzzy Systems Subject to Partially Decouplable Unknown Inputs

Local nonlinear fuzzy systems are useful for control solutions due to their ability to handle unmeasurable/inexact premise variables and reduce computational complexity. However, their estimation problems still require further development. This article addresses this issue by investigating set-membership estimation for a class of discrete-time local nonlinear uncertain Takagi-Sugeno fuzzy systems with guaranteed performance. We propose a new observer architecture that solves partially decouplable unknown inputs and converts nonlinear error dynamics into a linear parameter-varying type. Using the systematic ℓ _∞-technique, the design conditions in the form of linear matrix inequalities ensure stability and output performance of the state estimation. We also derive a straightforward and effective zonotopic analysis method, considering the fuzzy and local nonlinear context, for less conservative results without using any specific interval set computation. Furthermore, a fast fault detection logic is proposed as an application of the set-membership estimation. Finally, we demonstrate the feasibility and advantages of our approach through three compelling examples, showcasing its efficacy in different scenarios.