[Brief Paper] Reachable set estimation for linear systems in the presence of both discrete and distributed delays

The reachable set estimation for linear systems subject to both discrete and distributed delays is considered in this study. By choosing appropriate Lyapunov-Krasovkii functionals, some sufficient conditions are established to guarantee that all the states starting from the origin are bounded by an ellipsoid. The problem of finding the smallest possible ellipsoid can be transformed into an optimisation problem with matrix inequality constraints. Moreover, the computational complexity is reduced since fewer variables are involved in the obtained results. These criteria are further extended to systems with polytopic uncertainties. It is shown that in the absence of distributed delay, the obtained condition is also less conservative than the existing ones.