compreal

Companion realization of transfer functions.

Syntax

• [A, B, C, D, E] = compreal(numerator, denominator)

Input argument

• numerator - a vector or matrix
• denominator - a vector

Output 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.
• E (n x n) - matrix.

Description

[A, B, C, D, E] = compreal(numerator, denominator) calculates a state-space realization represented by matrices A, B, C, D, and E.

The E matrix is an empty matrix (identity matrix) when there are at least as many poles as zeros.

However, if there are more zeros than poles, the E matrix becomes singular.

Example

numerator = [0 10 10];
denominator = [1 1 10];
[A, B, C, D, E] = compreal(numerator, denominator)

See also

tf, ss, balance.

History

Author

Allan CORNET