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Linear systems with constant coefficients and time-varying delays are considered. We address the problem of finding an ellipsoid that bounds the set of the states (in the Euclidean space) that are reachable from the origin in finite time by inputs with peak value that is bounded by a prechosen positive scalar. The system may encounter uncertainties in the matrices of its state space model and in the delay length. The Lyapunov-Razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper-bound of the delay length.

Stability conditions for sampled-data nonlinear control system with linear output feedback are studied. The case of sector bounded nonlinearities and uncertain sampling with the known upper bound on the sampling intervals is considered. Stability analysis is performed by input delay approach based on time-dependent Lyapunov-Krasovskii functionals refined by Emilia Fridman in 2010 (Fridman's method) and extended by Seifullaev and Fradkov in 2013 to nonlinear control systems with sector bounded nonlinearity (Lurie systems). Based on classical results of V.A. Yakubovich about S-procedure the problem is reduced to feasibility analysis of linear matrix inequalities. Linear output feedback controller design is based on the Passification method. The results are illustrated by example showing that both bounds on the sampling interval and accuracy of those bounds depend essentially on the controller choice.