Derivation of LMI design conditions in switching fuzzy control

This paper presents controller design conditions based on a switching Lyapunov function in terms of linear matrix inequalities (LMIs) for switching fuzzy systems. In our previous papers, we proposed switching fuzzy model construction and derived switching fuzzy controller design conditions. However, the conditions have been given in terms of bilinear matrix inequalities (BMIs), so it is difficult to design the controller. In this paper, the conditions are given in terms of LMIs by introducing the augmented system which consists of a switching fuzzy model and a stable linear system. We can effectively design the switching fuzzy controller via a LMI-based approach. A design example illustrates the utility of this approach.