types.linearization.FullLinearization

types.linearization.FullLinearization

Complete linearization including output: (A, B, C, D).

Linearizes both dynamics and output equations.

State space form: Continuous: dx/dt = Acx + Bcu, y = Ccx + Dcu Discrete: x[k+1] = Adx + Bdu, y = Cdx + Ddu

Typically: - C is identity for full state observation - D is zero for no direct feedthrough

Examples

>>> A, B, C, D = system.full_linearization(x_eq, u_eq)
>>> 
>>> # State space model
>>> ss_continuous = scipy.signal.StateSpace(A, B, C, D)
>>> ss_discrete = scipy.signal.dlti(A, B, C, D, dt=0.01)
>>> 
>>> # Transfer function
>>> G_s = C @ np.linalg.inv(s*I - A) @ B + D

# types.linearization.FullLinearization { #cdesym.types.linearization.FullLinearization }

`types.linearization.FullLinearization`

Complete linearization including output: (A, B, C, D).

Linearizes both dynamics and output equations.

State space form:
    Continuous: dx/dt = Ac*x + Bc*u, y = Cc*x + Dc*u
    Discrete:   x[k+1] = Ad*x + Bd*u, y = Cd*x + Dd*u

Typically:
    - C is identity for full state observation
    - D is zero for no direct feedthrough

## Examples {.doc-section .doc-section-examples}

```python
>>> A, B, C, D = system.full_linearization(x_eq, u_eq)
>>> 
>>> # State space model
>>> ss_continuous = scipy.signal.StateSpace(A, B, C, D)
>>> ss_discrete = scipy.signal.dlti(A, B, C, D, dt=0.01)
>>> 
>>> # Transfer function
>>> G_s = C @ np.linalg.inv(s*I - A) @ B + D
```