Plenary lecture 1: on some properties of fuzzy systems
Constantin Voloşencu · International Conference on Signal Processing · 2009
The paper presents a short review of some main properties of fuzzy systems useful in control. Fuzzy rule bases and fuzzy systems may be seen as applications between real or fuzzy sets. They have algebraic properties as commutative law, neutral element and symmetric elements. The fuzzy systems, implemented using different rule bases, fuzzy values, membership functions, fuzzyfication and defuzzification methods have sector property. The paper is emphasising a spatial sector property, useful in stability analysis with Lyapunov techniques. The fuzzy systems may be characterised with SISO and MIMO transfer characteristics. These transfer characteristics are used in the pseudo-equivalence of the fuzzy PI controllers with linear PI controllers. The paper presents a way to use translated SISO transfer characteristics and gain characteristics of fuzzy blocks in the design of fuzzy control systems and stability analysis. Based on transient characteristics of fuzzy control systems some quality criteria are presented.