minreal

Minimal realization or pole-zero cancellation.

📝 Syntax

• [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)

📥 Input argument

• 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.

📤 Output argument

• Am, Bm, Cm, Dm - a minimal realization of the state-space system A, B, C, D.

• sysOut - a minimal realization of LTI input.

📄 Description

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.

💡 Example

sysIn = ss([1 0;0 -2], [-1;0], [2 1], 0, 3.2);
sysOut = minreal(sysIn)

🕔 History

Version	📄 Description
1.0.0	initial version