Finite-time sliding mode control for uncertain singular systems with one-side Lipschitz nonlinearities and time-varying delays

This paper primarily focused on a finite-time sliding mode control (SMC) problem for uncertain singular systems with OSL nonlinearities. Under the condition of a suitable SMC law, a time-division strategy is used to divide the time interval [0, T] into two phases, which are the arrival phase \([0, T^*]\) $[0,T^{\ast }]$ and the sliding motion phase \([T^*, T]\) $[T^{\ast },T]$ , respectively. Firstly, it is proved that the time \(T^*\) $T^{\ast }$ to reach the sliding mode surface is less than T. Secondly, it is proved that uncertain singular systems with OSL nonlinearities are regular and impulse-free. Whereafter, the related conditions are derived to guarantee that the system satisfies singular sliding mode finite-time boundedness (SSMFTB) during the whole phase [0, T]. Next, the controller and observer gain matrices can be computed in term of the linear matrix inequality (LMI) method. Lastly, numerical examples are presented to demonstrate the effectiveness of the proposed new design schemes.