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

Abstract

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 paper 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _\infty$</tex-math></inline-formula> -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.