Uniformly Continuous Generalized Sliding Mode Control

This paper explores a general class of singular kernels with the objective of designing new families of uniformly continuous sliding mode controllers. The proposed controller results from filtering a discontinuous switching function by means of a Sonine integral, producing a uniformly continuous control signal, preserving finite-time sliding motion and robustness against continuous but unknown and not necessarily integer-order differentiable disturbances. The principle of dynamic memory resetting is considered to demonstrate finite-time stability. A set of sufficient conditions to design singular kernels, preserving the above characteristics, is presented, and several examples are exposed to propose new families of continuous sliding mode approaches. Simulation results are studied to illustrate the feasibility of some of the proposed schemes.