Abstract
In this study, we investigate the reachable set estimation for linear systems with discrete delay and distributed delay as well as disturbances. Based on the reciprocally convex combination lemma, free-weighting matrix approach and convex analysis technique, improved delay-dependent linear matrix inequalities (LMIs) criteria are derived for finding an ellipsoid to bound the reachable sets of such systems. Moreover, this result is extended to the one for linear systems with discrete delay, distributed delay and disturbances as well as polytopic-type uncertainties. In addition, the proposed results include some existing ones as special cases since the initial conditions of the systems are not required to be zero. Finally, two numerical examples are provided to show that our results have less conservative.
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