Membership-dependent polynomial fuzzy control of a positive discrete time system: A symbol transfer technique

This work explores the polynomial fuzzy stabilization for positive systems. The traditional quadratic Lyapunov function and basic stability analysis may not be favourable for stability investigation due to the absence of the positivity property and membership functions. Therefore, a fuzzy co-positive polynomial Lyapunov–Krasovskii (FCPL) function which considers the positivity is proposed firstly through an imperfect premise matching (IPM) approach. Secondly, the symbol transfer technique which takes into account fuzzy membership knowledge relaxes the stability conditions. The number of symbols is reduced by two constraints: (1) the last and next moments of the membership functions of the FCPL function; (2) membership functions of the fuzzy model and the controller. Finally, the polynomial fuzzy controller with symbols is obtained. Two examples are implemented to verify the proposed methods.