Switching law design for finite-time stability of singular fractional-order systems with delay

In this study, the authors present an analytical approach based on the Laplace transform and 'inf-sup' method for studying the finite-time stability of singular fractional-order switched systems with delay. A constructive geometric design for switching laws based on the construction of a partition of the stability state regions in convex cones is proposed. Using the proposed method, new delay-dependent sufficient conditions for regularity, impulse-free and finite-time stability of the system are developed in terms of tractable matrix inequalities and Mittag-Leffler functions. An example is provided to illustrate the effectiveness of the proposed method.