New Criteria of Reachable Set Estimation for Time Delay Systems Subject to Polytopic Uncertainties

The problem of reachable set estimation for linear systems subject to both time delay and polytopic uncertainties is considered in this paper. Our aim is to find a set as small as possible to bound the states starting from the origin by inputs with peak values. The Lyapunov-Krasovskii functional together with free-weighting matrix technique are proposed to derive some sufficient conditions for the existence of an ellipsoidal bound to estimate the states. This method eliminates the conservatism generated by Jensen's inequality and obtains a much tighter reachable set bound. In addition, the number of variables to be determined is smaller than the previous result based on the maximal Lyapunov functional. Finally, an example illustrates the merits of our proposed results.