Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

By Antoine Girard, C. J. Guernic, Oded Maler. International Conference on Hybrid Systems: Computation and Control, 2006

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Formal verification of hybrid systems (2011, methodology): “Representation using zonotopes and support functions [22,26] has so far resulted in the most scalable approach for the analysis of linear hybrid systems, leading to the tool SpaceEx that is able to analyze, for instance, a complex 28-dimensional helicopter controller [20].”
Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, methodology): “For linear systems with uncertain input, zonotopes [69, 72, 100] and support functions [70] have clearly outperformed existing methods, allowing the verification of systems with more than 100 continuous state variables.”
SpaceEx: Scalable Verification of Hybrid Systems (2011, methodology): “A new algorithm based on a “lazy” representation of the reachable sets, first developed for the special case where reachable states are represented by Zonotopes [10] and then extended and crystalized using the more general representation via support functions [14,13,15], has dramatically increased t”