Robust stability constraints for fuzzy model predictive control

This paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the Takagi–Sugeno (T–S) type, resulting in a stable closed-loop control system. Conditions are given that guarantee closed-loop robust asymptotic stability for open-loop bounded-input–boundedoutput (BIBO) stable processes with an additive 1-norm bounded model uncertainty. The idea is closely related to (small-gain-based) 1-control theory, but due to the time-varying approach, the resulting robust stability constraints are less conservative. Therefore the fuzzy model is viewed as a linear time-varying system rather than a nonlinear one. The goal is to obtain constraints on the control signal and its increment that guarantee robust stability. Robust global asymptotic stability and offset-free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances.