Abstract In this paper we consider stability analysis and controller design for periodic Takagi–Sugeno fuzzy models. To develop the conditions, we use a switching nonquadratic Lyapunov function defined at the time instants when the subsystems switch. Using the proposed conditions we are able to handle periodic Takagi–Sugeno systems where the local models or even the subsystems are unstable or cannot be stabilized. The application of the conditions is illustrated on numerical examples.