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This work is further focused on analyzing a bound for a reachable set of linear uncertain systems with polytopic parameters. By means of L-K functional theory and novel inequalities, some new conditions which are expressed in the form of LMIs are derived. It should be noted that novel inequalities can improve upper bounds of Jensen inequalities, which yields less conservatism of systems. Consequently, some numerical examples demonstrate that the authors’ results are somewhat more effective and advantageous compared with the previous results.

New results on reachable set bounding for linear time delay systems with polytopic uncertainties via novel inequalities