Fixed/predefined-time stability and designing of terminal sliding mode control of impulsive dynamical systems

The contribution of the present work is two-fold. Firstly, some results on the predefined and fixed-time stability of non-linear impulsive systems are derived. Impulse-dependent sufficient conditions are derived for predefined-time estimation of settling-time under the influence of stabilising impulses. In contrast, a fixed-time estimate of the settling-time is obtained for destabilising impulses. Secondly, terminal sliding mode (TSM) control is designed in the presence of hybrid (continuous and impulsive) matched disturbances for n-dimensional systems. It shows that the trajectories can reach the sliding surfaces in fixed-time and thus will stay on it after that under the influence of the proposed TSM. Thus, the system states will converge to the origin in a fixed-time. Finally, three examples, which also consist of the stability of Cohen-Grossberg BAM neural networks, are provided to justify the proposed results numerically.