systems.builtin.deterministic.continuous.LinearSystem

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

First-order linear system: dx/dt = -ax + bu

Canonical example for testing and learning.

Parameters

Name	Type	Description	Default
a	float	State coefficient (positive = stable)	`1.0`
b	float	Control gain	`1.0`

Examples

>>> system = LinearSystem(a=2.0, b=1.0)
>>> x = np.array([1.0])
>>> u = np.array([0.5])
>>> dx = system(x, u)  # -2*1 + 1*0.5 = -1.5

Methods

Name	Description
define_system	Define linear system dynamics.

define_system

systems.builtin.deterministic.continuous.LinearSystem.define_system(
    a=1.0,
    b=1.0,
)

Define linear system dynamics.

# systems.builtin.deterministic.continuous.LinearSystem { #cdesym.systems.builtin.deterministic.continuous.LinearSystem }

```python
systems.builtin.deterministic.continuous.LinearSystem(*args, **kwargs)
```

First-order linear system: dx/dt = -a*x + b*u

Canonical example for testing and learning.

## Parameters {.doc-section .doc-section-parameters}

| Name   | Type   | Description                           | Default   |
|--------|--------|---------------------------------------|-----------|
| a      | float  | State coefficient (positive = stable) | `1.0`     |
| b      | float  | Control gain                          | `1.0`     |

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

```python
>>> system = LinearSystem(a=2.0, b=1.0)
>>> x = np.array([1.0])
>>> u = np.array([0.5])
>>> dx = system(x, u)  # -2*1 + 1*0.5 = -1.5
```

## Methods

| Name | Description |
| --- | --- |
| [define_system](#cdesym.systems.builtin.deterministic.continuous.LinearSystem.define_system) | Define linear system dynamics. |

### define_system { #cdesym.systems.builtin.deterministic.continuous.LinearSystem.define_system }

```python
systems.builtin.deterministic.continuous.LinearSystem.define_system(
    a=1.0,
    b=1.0,
)
```

Define linear system dynamics.