Stability Analysis of Positive Interval Type-2 TSK Systems With Application to Energy Markets

Positive systems play an important role in many fields including biology, chemistry, and economics, among others. This paper discusses the stability of interval type-2 discrete-time positive Takagi-Sugeno-Kang (TSK) fuzzy systems. It discusses positive TSK systems and their nonzero equilibrium point. It then provides sufficient conditions for their exponential stability and instability. All the proposed stability and instability conditions can be tested using linear matrix inequalities. The stability and instability tests are demonstrated through application to a TSK model of the electric power market under a variety of market conditions.