Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances

This paper investigates the finite-time and fixed-time stabilization (FFTS) of switched systems with discontinuous dynamics, external disturbances and delays. Firstly, a new parameterized discontinuous stabilizer is designed to ensure the FFTS of switched discontinuous systems in the sense of Filippov solutions. Secondly, a detailed analysis is provided on how to regulate the power parameters to determine the settling time is finite or fixed. Thirdly, a new adaptive controller is further designed to stabilize the considered system in a finite time, and the corresponding settling time is estimated as well. Finally, two examples are given to demonstrate the efficiency of the proposed method.