types.control_advanced.H2ControlResult

types.control_advanced.H2ControlResult()

H₂ optimal control result.

H₂ control minimizes the RMS (root-mean-square) response to white noise disturbances, equivalent to LQG for certain problem setups.

Fields

gain : GainMatrix H₂ optimal controller gain K (nu, nx) h2_norm : float Achieved H₂ norm ‖G‖₂ cost_to_go : CovarianceMatrix Riccati solution P (nx, nx) closed_loop_stable : bool Closed-loop system is stable closed_loop_poles : np.ndarray Eigenvalues of (A - BK)

Examples

>>> # Design H₂ controller
>>> A = np.array([[0, 1], [-2, -3]])
>>> B = np.array([[0], [1]])
>>> C_z = np.eye(2)  # Performance output
>>> D_zu = np.zeros((2, 1))
>>>
>>> result: H2ControlResult = design_h2_controller(A, B, C_z, D_zu)
>>>
>>> K = result['gain']
>>> print(f"H₂ norm: {result['h2_norm']:.3f}")
>>> print(f"Stable: {result['closed_loop_stable']}")
>>>
>>> # Apply control
>>> u = -K @ x

# types.control_advanced.H2ControlResult { #cdesym.types.control_advanced.H2ControlResult }

```python
types.control_advanced.H2ControlResult()
```

H₂ optimal control result.

H₂ control minimizes the RMS (root-mean-square) response to
white noise disturbances, equivalent to LQG for certain problem setups.

## Fields {.doc-section .doc-section-fields}

gain : GainMatrix
    H₂ optimal controller gain K (nu, nx)
h2_norm : float
    Achieved H₂ norm ‖G‖₂
cost_to_go : CovarianceMatrix
    Riccati solution P (nx, nx)
closed_loop_stable : bool
    Closed-loop system is stable
closed_loop_poles : np.ndarray
    Eigenvalues of (A - BK)

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

```python
>>> # Design H₂ controller
>>> A = np.array([[0, 1], [-2, -3]])
>>> B = np.array([[0], [1]])
>>> C_z = np.eye(2)  # Performance output
>>> D_zu = np.zeros((2, 1))
>>>
>>> result: H2ControlResult = design_h2_controller(A, B, C_z, D_zu)
>>>
>>> K = result['gain']
>>> print(f"H₂ norm: {result['h2_norm']:.3f}")
>>> print(f"Stable: {result['closed_loop_stable']}")
>>>
>>> # Apply control
>>> u = -K @ x
```