Passivity-based robust adaptive sliding mode control for singular time-delay systems with uncertainties in both derivative matrix and some other system matrices

This article addresses the passivity analysis and passification problems for a class of nonlinear singular time-varying delay systems with the special forms of uncertainties in both derivative matrix and some other system matrices by adopting adaptive sliding mode control (SMC) strategy. First, a distinctive state augmentation technique, which keeps the admissibility and the robust passivity unchanged, is employed due to "left-singular" form uncertainty in the derivative matrix (ie, E0(I+Delta E0(sigma))). Next, an integral-type sliding surface, which involves the SMC gain matrix K, is constructed. By designing an appropriate Lyapunov-Krasovskii functional and introducing slack matrix approach, in which the slack matrix W similar to is not constrained in contrast to most existing literatures, a new sufficient condition is derived to ensure that the resulting sliding mode dynamics is admissible and robustly passive for all admissible uncertainties. Additionally, for the passification problem, a delay-dependent sufficient condition is proposed in the form of strict linear matrix inequality (LMI), which not only removes the equality constraint but also makes the SMC gain matrix K solvable. Then a novel adaptive SMC law, which does not need to use the assumption that bounds of nonlinear perturbation function and external disturbance are known constants, is synthesized such that the finite-time reachability can be guaranteed. And the state information before and after state augmented transformation is utilized in SMC law design to help achieve better performance. Finally, four examples are presented to illustrate the effectiveness, superiority, and less conservativeness of the proposed scheme.