This paper addresses the problem of bounding the reachable set of the sliding dynamics in discrete-time systems subject to time-varying state delay and bounded external disturbances. The sliding motion is determined from the equivalent dynamics chosen from a desired eigen-structure via the pole placement technique. New delay-dependent conditions are derived to guarantee that the trajectories in the sliding mode are prescribed in an ellipsoid with a minimal bound on each coordinate.

This paper addresses the problem of reachable set bounding for linear systems in the presence of both discrete and distributed delays. The time delay is assumed to be differentiable and vary within an interval.

This paper addresses the problem of reachable set bounding for linear discrete-time systems that are subject to state delay and bounded disturbances. Based on the Lyapunov method, a sufficient condition for the existence of ellipsoid-based bounds of reachable sets of a linear uncertain discrete system is derived in terms of matrix inequalities. Here, a new idea is to minimize the projection distances of the ellipsoids on each axis with different exponential convergence rates, instead of minimization of their radius with a single exponential rate.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate.