A passivity framework for fuzzy control system stability: case of two-input-single output fuzzy-controllers

The paper presents a passivity framework to analyse the asymptotic stability of zero-steady-state error solutions of fuzzy control systems. Typical two-input-single-output fuzzy, controllers (FC) are considered for which we propose a continuous-time single input nonlinear dynamic representation based on a pseudo-derivative of the error. The nonlinear part is a two-input mapping with a set of properties arising from the mini or product-inference rule, as well as properties of the input and output fuzzy sets used. The stability analysis is performed for the class of linear time invariant plant models with PI-like FC, it is based on general results coming from positive real and passive systems, leading to two graphical tests. Hints are given to deal with the case of PD-like FC.