Christian Schilling

See [here](https://en.wikipedia.org/wiki/Matrix_exponential#Using_the_Jordan_canonical_form). This could be fast if the matrix was already in Jordan form. Otherwise, it might suffer from numerical issues. Also note that the reals are not algebraically closed,...

Given that we have an algorithm for linear hybrid dynamics (#138), we can add hybridization algorithms which approximate nonlinear continuous systems by linear hybrid systems by state space partitioning. ---...

Currently the hybrid loop lives in `solve.jl`. I suggest we outsource it to a new file in the `ReachSets` module.

The first idea in #331 was that this was in general more precise, which it is not. But it might be a nice feature to apply the intersection only *after*...

If there is no assignment, then the intersection with the two invariants and the guard can be statically precomputed. Then we only have to take a single intersection. Ideally, this...

Understand why 1D analysis is slower than nD analysis

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This is at least true for ISS: With lazy inputs: 18.53 seconds (1D) vs. 0.35 seconds (270D) Without lazy inputs: 13.51 seconds (1D) vs. 11.97 seconds (270D) So the lazy...

Handling of Zeno behavior

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After we have an algorithm for hybrid systems in #138, we might face the problem of [Zeno behavior](https://en.wikipedia.org/wiki/Zeno%27s_paradoxes), i.e., infinitely many discrete jumps in finite time. I got the suggestion...

If there is a time variable that is never reset, this dimension grows monotonically and hence we can never find a fixpoint. Options: * Handle time separately (#263). * Let...

Add a bound to clustering.

Low-dimensional discrete-post operator

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Terminology: An *embedded set* is a high-dimensional set that is universal in some dimensions. Let `U(m)` be the `m`-dimensional universal set. Then I am talking about a set `U(k) ×...