On stabilization of discrete-time periodic TS systems

Abstract—In this paper we consider controller design for periodic Takagi-Sugeno fuzzy models. For this, we use a periodic 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. Index Terms—Takagi-Sugeno fuzzy models, controller design, periodic systems, nonquadratic Lyapunov function I