Stabilization of nonstandard singularly perturbed systems with small delays in state and control

A nonstandard singularly perturbed linear time-invariant system with a general type of small delay in state and control variables is considered. Two much simpler parameter-free systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. Since the original system is nonstandard, the reduced-order one is descriptor (differential-algebraic). A composite feedback control exponentially stabilizing the original system is constructed based on stabilizing controls of the reduced-order and boundary-layer systems. An illustrative example is presented.