Software
Reachability analysis
Reachability analysis based on set propagation
In Matlab
- Multiparametric Toolbox (MPT): https://www.mpt3.org
- Some functionality (invariant set computation) purely for discrete-time systems
- CORA: https://tumcps.github.io/CORA/
- Supports also continuous-time systems, and not only linear but also nonlinear and hybrid ones.
Quite a few other tools can be found on the web but mostly unmaintained.
In Julia
- ReachabilityAnalysis.jl: https://juliareach.github.io/ReachabilityAnalysis.jl/
In Python
- Sorry, I am not aware of anything, but I will gladly add whatever you suggest. Just keep in mind that the tool should be actively maintained to be useful at least for study purposes.
Barrier certificates
No specialized software. At the moment just the same computational tools as for Lyapunov stability analysis – nonnegative (sum-of-squares) polynomial optimization, etc.