Python script that uses the simpy library to simulate a system with Lyapunov stability control. The script defines a simple dynamical system and uses a Lyapunov function to demonstrate stability. This script sets up a simpy environment and simulates the behavior of a linear system with a negative definite matrix A. The Lyapunov function used here is simply the quadratic form ( V(x) = x^T x ), which is a common choice for linear systems. The script checks the derivative of the Lyapunov function to determine if the system is stable.
Remember to adjust the system matrix A and the simulation time as needed for your specific use case. Also, this is a simplified example, and real-world applications may require more complex models and Lyapunov functions.