A tighter reachable set bound for linear systems subject to both discrete and distributed delays

The problem of reachable set bounding for a class of linear systems subject to both discrete and distributed delays is addressed in this paper. First, a new criterion is derived to give an ellipsoid which bounds all the states starting from the origin by inputs with peak-values. The constraint with a special structure that appeared in our previous result is removed by combining the Jensen integral inequality and the reciprocally convex approach. In addition, the obtained condition brings a tighter reachable set estimation with lower computational complexity. We also extend the above result to systems with polytopic uncertainties. Finally, an example is presented to illustrate the merit of our proposed method.