Relative Controllability and Finite Interval Stability of Impulsive Fractional Order Switched Delay Differential System with Nonlinear Perturbation

The manuscript examines a class of switched fractional order system with time-varying delays occurring at different time instant in the state and control input. Initially, we substantiate the relative controllability of the nonlinear system by incorporating the technique of delayed Mittag–Leffler function to construct the Grammian matrices. In addition to this, fixed point argument is utilized to manipulate the required controllability criteria of the system. Further, the necessary bound for the finite time stability of the system is estimated by implementing Gronwall’s integral inequality. Conclusively, we establish the application of our theoretical study by providing illustrative examples.