Robust stabilizability and stabilization of three-time-scale linear time-invariant singularly perturbed systems with delay

The objective of this study is to obtain the stabilizability conditions and a stabilizing composite state feedback control for exponential stabilization three-time-scale singularly perturbed linear time-invariant systems with multiple commensurate delays in slow variables two small parameters perturbation (TSPLTISD). do not depend on are valid all their sufficiently values. approach used work nondegenerate decoupling transformation that splits TSPLTISD into three regularly dependent subsystems, which lower dimensions than TSPLTISD. Further, decoupled subsystems approximated by parameters. It proven approximating guarantees robust (with respect parameters) original Finally, we representation parameter free TSPLTISD, it values A numerical example given.