systems.builtin.deterministic.continuous.LinearSystem2D

systems.builtin.deterministic.continuous.LinearSystem2D(*args, **kwargs)

Two-dimensional linear system.

Dynamics: dx1/dt = a11x1 + a12x2 + b1u dx2/dt = a21x1 + a22x2 + b2u

Parameters

Name	Type	Description	Default
a11	float	State matrix coefficients	required
a12	float	State matrix coefficients	required
a21	float	State matrix coefficients	required
a22	float	State matrix coefficients	required
b1	float	Control gain coefficients	required
b2	float	Control gain coefficients	required

Examples

>>> # Stable spiral
>>> system = LinearSystem2D(
...     a11=-1, a12=2, a21=-2, a22=-1, b1=1, b2=0
... )
>>> eigenvalues = np.linalg.eigvals(np.array([[-1, 2], [-2, -1]]))
>>> # λ = -1 ± 2j (stable spiral)

Methods

Name	Description
define_system	Define 2D linear dynamics.

define_system

systems.builtin.deterministic.continuous.LinearSystem2D.define_system(
    a11=-1.0,
    a12=0.0,
    a21=0.0,
    a22=-1.0,
    b1=1.0,
    b2=0.0,
)

Define 2D linear dynamics.