Discretize Continuous State Space Model

Implement a discretization method for State Space Models originally defined in continuous time to accommodate discrete token sequences. This process is crucial for applying continuous-time models to real-world problems that involve discrete data.

The Continuous State Space Model is defined by the equations $x'(t) = Ax(t) + Bu(t)$ and $y(t) = Cx(t)$, where $x(t)$ is the state vector, $u(t)$ is the input vector, and $y(t)$ is the output vector. To discretize this model, we can use the Zero-Order Hold method, which assumes the input is constant between sampling times.

Here are the steps to discretize the model:

1. Define the continuous-time model parameters $A$, $B$, and the sampling time $\Delta$.
2. Compute the discretized state transition matrix $\bar{A}$ and input coefficient $\bar{B}$.

This technique is widely used in digital control systems.