Stability and stabilisability of the singularly perturbed system with delay on time scales: a decomposition approach

Sufficient conditions for the exponential stability and stabilisability of linear singularly perturbed control systems with the small parameter defined on homogeneous time scale are studied. Stability conditions are formulated in terms of a spectrum of two parameter-free subsystems of lower dimensions than the original one: slow and fast subsystems. These conditions, being parameter-free, provide the exponential stability of the original singularly perturbed system with delay for all sufficiently small positive values of parameter, i.e. robust with respect to the parameter of singular perturbation. A stabilisation problem for a given class of control systems is solved by a design of a linear well-conditioned parameter-free composite state-feedback control which is a sum of a stabilising slow and fast control. © 2021 Informa UK Limited, trading as Taylor & Francis Group.