Dynamic non-idealities and their effect on the asymptotic behavior of discrete variable structure control systems with delays

In this paper, the exponential stability of the discrete linear singularly perturbed system with delay is studied by the space decomposition and systematic method. Based on the invariance criterion for the set Ω_α of cone type and some structural transformations, some sufficient conditions have been formulated and small parameter estimates obtained that would guarantee the exponential stability of discrete variable structure systems (VSS) with delay and a discontinuous right-hand side. It is has been established, in particular, that the VSS with delay robust to regular perturbations are always robust to singular ones. The absolute stable robustness to dynamical nonidealities has been established for discrete time-invariant system with delay