Demo_discrete_time_stability_proof

A demonstration of a numerical method to prove the exponential stability of nonlinear high-dimensional discrete-time systems and to find positive invariant ellipsoids. Link to related paper https://hal.science/hal-04465206v1 There are two executable main files Dependencies: numpy, scipy, sympy, matplotlib and codac

main_guaranteed_computation.py

The main file of the demo - all operations are guaranteed with intervals

The first part of the script defines the discrete-time systems. some parameters can be tuned. The second part of the script proves the exponential stability of the system and finds a positive invariant ellipsoid

This second part uses the ellipsoidal propagation method presented in [Add the link]

The method can be too pessimistic and raise an error.

The ellipsoids are plotted at the end

main_fast_computation.py

an optional file. the matrix inversion and the matrix square root are not guaranteed. The algorithm is much faster but not guaranteed

lib.py

A toolbox for the main files