Stability on type-1 and type-2 fuzzy logic systems

Abstract

The fuzzy systems present some characteristics that the classical control systems (PI, PD and PID) don't have, like smoother control, noise immunity, important mathematical complexity reduction, little mathematical knowledge of the model work, and they can obtain results from imprecise data. Broadly stated, fuzzy logic control attempts to come to terms with the informal nature of the control design process. In its most basic form, the so-called Mamdani architecture is directly translating external performance specifications and observations of plant behavior into a rule-based linguistic control strategy. This architecture forms the backbone of the great majority of fuzzy logic control systems reported in the literature in the past years. This paper is based on the fuzzy Lyapunov synthesis, to determine the systems stability, which is based on the Lyapunov criterion; this concept was introduced by Margaliot to adjust the Lyapunov criteria by considering linguistic variables instead of numeric variables to determine the systems stability. The stability will be proving on Mamdani's architecture fuzzy logic systems type-1 and type-2 respectively. © 2008 Springer-Verlag Berlin Heidelberg.