Exponential Stability Criteria for Fractional Order Switched System Based on Multiple Discontinuous Lyapunov Function Method

In this article, the exponential stability of Caputo fractional order switched system (CFOSS) that simultaneously includes unstable and stable subsystems is discussed. By combining the mode-dependent average dwell time (MDADT) technique with the multiple discontinuous Lyapunov functions (MDLF) method, the sufficient, low-conservatism conditions for such stability are obtained, and then the conditions are applied to Caputo fractional order linear switched system (CFOLSS) to derive a set of algebraic criteria for solvable linear matrix inequalities (LMIs). Next, the criteria for stability of the switched T-S fuzzy model under rapid and slow MDADT switching are determined by representing the underlying nonlinear system using the T-S fuzzy modeling approach. The findings verify that CFOSS with unstable subsystems and stable subsystems is exponentially stable when the stable subsystems stay long enough or when all unstable subsystems switch quickly enough. Ultimately, the efficacy of the result is validated via two numerical simulation examples provided.