Robust $(\mathcal{Q},\mathcal{S},\mathcal{R})$-$\gamma$-dissipative sliding mode control for uncertain discrete-time descriptor systems with time-varying delay

In this study, a robust sliding mode-based learning control strategy for a class of non-linear discrete-time descriptor systems with time-varying delay and external disturbance is developed. A new sliding function is proposed and a sufficient condition is derived to guarantee the sliding mode dynamics to be robustly admissible and |$(\mathcal{Q},\mathcal{S},\mathcal{R})$|-|$\gamma$|-dissipative. Moreover, a sliding-mode control law is proposed such that the reaching motion satisfies the discrete-time sliding mode reaching condition for all admissible uncertainties and time-varying delay. The appealing attributes of this approach include: (i) the closed-loop system exhibits a strong robustness against uncertain dynamics and (ii) the control scheme enjoys the chattering-free characteristic. Two representative examples are given to illustrate the theoretical developments.