Gunther Reissig.
Over-Approximation of Reachable Sets of LTI Systems Using A Posteriori Information
Proc. 64rd IEEE Conf. Decision and Control (CDC), Rio de Janeiro, Brazil, 10-12 Dec. 2025, pp. 899-904.

Abstract:
We present a method to approximate output reachable sets at time points, for continuous-time LTI systems, where the initial state lies in a compact convex uncertainty set and the input signal takes values in a zonotopic uncertainty set at each point in time. Our focus is on over-approximations. We present an interval over-approximation margin and derive bounds on the approximation error that improve upon our previous work, in part through the use of a posteriori information. The error exhibits second-order convergence with respect to a discretization parameter. Our method significantly outperforms existing approaches across a wide range of approximation accuracies, as demonstrated on several examples.

BibTeX entry:

@InProceedings{Reissig24bC,
 author = {Gunther Reissig},
 title = {Over-Approximation of Reachable Sets of {LTI} Systems Using A Posteriori Information},
 booktitle = {Proc. IEEE Conf. Decision and Control (CDC), Rio de Janeiro, Brazil, 10-12 } # dec # { 2025},
 pages = {899-904},
 year  = {2025},
 doi   = {}
}

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