Stability Results for Caputo Fractional Order Synchronous Variable Order Nonlinear Discrete-Time Switched Systems

Fractional non-continuous switched systems are delineated by one category of difference systems. Those distinguished by operators indicating non-integer differences. In spite of the fact that there have been many successful achievements in the stable of constant switched systems, there turned out to be a scarcity of publications on this subject. Our paper mainly solves the finite time stability problem of a form of fractional order synchronous variable order nonlinear switched systems based on a unique Nabla Caputo discrete operator. In addition, a representation of short-memory fractional order synchronous variable order nonlinear discrete switched systems is proposed, and then one innovative theorem is proposed to demonstrate its asymptotic stability. Finally, instances are showcased to illustrate the efficacy of the findings.