tf2ss

Convert transfer function filter parameters to state-space form.

Syntax

• [A, B, C, D] = tf2ss(b, a)

Input argument

• b - Transfer function numerator coefficients: vector or matrix.
• a - Transfer function denominator coefficients: 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.

Description

[A, B, C, D] = tf2ss(b, a) transforms a single-input transfer function, either continuous-time or discrete-time, into an equivalent state-space representation.

Example

Fs = 6;
dt = 1/Fs;
b = [1 -(1+cos(dt)) cos(dt)];
a = [1 -3*cos(dt) 1];
[A, B, C, D] = tf2ss(b, a)

See also

ss2tf, ss, tf.

History

Author

Allan CORNET