Reachable set estimation for continuous delayed singularly perturbed systems with bounded disturbances.

• Considering only a rough boundary of the singularly perturbed parameter κ is available, the bounding ellipsoid obtained this paper is independent on κ such that this ellipsoid can comprise the reachable set of this system for any admissible singularly perturbed parameters. • A κ -dependent LKF is constructed by unequally dividing the delay into two sub-intervals to lead to more superior criteria for the reachable set estimation. • The conditions derived are all independent on the singularly perturbed parameter κ to avoid ill-conditioned numerical trouble. Reachable set estimation problem in allusion to continuous-time singularly perturbed systems that take on time-varying delays and bounded disturbances is discussed in this paper. In many singularly perturbed systems, since the perturbed parameter κ is not available, our task is to determine an ellipsoid as small as possible which can be independent on κ. In this case, for any admissible singularly perturbed parameters, this ellipsoid can surround the states of the system. First, in order to obtain more accurate result, the delay is unequally divided into two sub-intervals and a κ -dependent Lyapunov-Krasocskii functional is established. Then, with the aid of reciprocally convex inequality for each sub-interval, sufficient delay-dependent conditions are established which can make the system states contained by a κ -independent ellipsoid. Finally, a numerical example is given to verify the validity of the result. [ABSTRACT FROM AUTHOR]