Predefined-time stability and its applications using non-singular sliding mode control

Abstract

In this work, a Lyapunov-like sufficient condition for predefined-time stability PDTS is presented for a class of dynamical systems. In addition, the proposed Lyapunov-like condition allows us to deduce some prior results on PDTS. Based on the proposed scheme, non-singular predefined-time controllers are designed for first-order systems. Further, a predefined-time terminal sliding surface PDTSS and corresponding non-singular predefined-time terminal sliding mode control NPDTSM strategy have been proposed for the second-order systems. These controllers have several advantages: (i) The control scheme can withstand the effects of bounded, non-vanishing disturbances and is non-singular in the whole state space. (ii) The convergence time can be specified by a constant defined by the user in advance. Along with the predefined-time synchronization of the Φ6 duffing oscillator, a two-dimensional chaotic system, some examples are provided to justify the numerical inferences of the proposed scheme.