[Am, Bm, Cm, Dm] = minreal(A, B, C, D)
[Am, Bm, Cm, Dm] = minreal(A, B, C, D, tol)
sysOut = minreal(sysIn)
sysOut = minreal(sysIn, tol)
| Parameter | Description |
|---|---|
| A (n x n) | Represents the system's state-transition matrix. It describes how the system's internal state evolves over time. |
| B (n x m) | Describes the input-to-state mapping. It shows how control inputs affect the change in the system's state. |
| C (p x n) | Represents the state-to-output mapping. It shows how the system's state variables are related to the system's outputs. |
| D (p x m) | Describes the direct feedthrough from inputs to outputs. In many systems, this matrix is zero because there is no direct feedthrough. |
| tol | scalar real (tolerance). |
| sysIn | LTI model. |
| Parameter | Description |
|---|---|
| Am, Bm, Cm, Dm | a minimal realization of the state-space system A, B, C, D. |
| sysOut | a minimal realization of LTI input. |
minreal function reduces state-space models by eliminating uncontrollable or unobservable states.
In transfer functions or zero-pole-gain models, it cancels pole-zero pairs. The resulting model maintains the same response characteristics as the original model but with minimal order.
When using sysOut = minreal(sysIn, tol), you can customize the tolerance for state elimination or pole-zero cancellation.
The default tolerance is set to sqrt(eps), and increasing this value prompts more aggressive cancellations, potentially further simplifying the model.
sysIn = ss([1 0;0 -2], [-1;0], [2 1], 0, 3.2);
sysOut = minreal(sysIn)| Version | Description |
|---|---|
| 1.0.0 | initial version |