Predefined-time adaptive robust simultaneous stabilisation control for two nonlinear singular time-delay systems

This paper mainly studies the simultaneous stabilisation control problem of a class of nonlinear singular systems with predefined time. We first develop two singular system in differential algebraic forms via an appropriate state feedback. And then the two systems are extended to one system for further research. We have solved the difficulty of constructing Lyapunov functions by constructing appropriate Hamiltonian functions for our research. In addition, when considering nonlinear singular systems with unknown disturbances, parameter uncertainties and time delays, a control strategy is developed to achieve simultaneous stabilisation within a predefined time. Finally, the effectiveness of the proposed controller was verified through simulation.