tf — Create and combine SISO transfer-function model objects.

tf('s') creates a continuous-time transfer-function variable, and tf(num, den) creates scalar-input scalar-output transfer-function objects from numeric coefficient vectors. Coefficients follow MATLAB-compatible highest-order-to-constant polynomial ordering.

Syntax

s = tf('s')
z = tf('z', Ts)
sys = tf(numerator, denominator)
sys = tf(numerator, denominator, Ts)
sys = tf(numerator, denominator, "Variable", variableName)
sys = tf(numerator, denominator, name, value, ...)

Inputs

Returns

Errors

How tf works

• tf('s') and tf('p') create continuous-time transfer-function variables with numerator [1 0], denominator [1], and Ts = 0.
• tf('z', Ts), tf('q', Ts), tf('z^-1', Ts), and tf('q^-1', Ts) create discrete-time variables with a positive sample time.
• Accepts numeric scalar, row-vector, or column-vector numerator coefficients.
• Accepts numeric scalar, row-vector, or column-vector denominator coefficients.
• Normalizes stored numerator and denominator coefficients to row vectors on the returned tf object.
• Returns a lightweight object whose class name is tf.
• Stores Numerator, Denominator, Variable, Ts, InputDelay, and OutputDelay properties on the object.
• Uses continuous-time defaults: Variable is 's' and Ts is 0.
• tf(num, den, Ts) stores a finite non-negative sample time and defaults Variable to 'z'.
• tf(num, den, 'Variable', variable) accepts variable values 's', 'p', 'z', 'q', 'z^-1', and 'q^-1'.
• tf(num, den, 'Ts', Ts) or tf(num, den, 'SampleTime', Ts) stores a finite non-negative sample time.
• Complex coefficients are accepted and stored as complex row vectors.
• Logical and integer coefficients are promoted to double precision.
• tf objects overload +, -, unary +, unary -, *, .*, /, ./, \, .\, ^, and .^ for SISO transfer-function algebra with scalar gains.
• Transfer-function powers require integer scalar exponents.
• Arithmetic requires compatible sample times and does not support nonzero input or output delays.

GPU memory and residency

tf is a host-side object constructor. gpuArray coefficient inputs are gathered before object construction, and the returned transfer-function object does not live on the GPU.

Examples

Using the transfer-function variable shorthand

s = tf('s');
G = 2.5/(0.4*s^2 + 1.8*s + 1);
G.Denominator

Expected output:

ans = [0.4 1.8 1.0]

Creating a first-order continuous-time transfer function

H = tf(20, [1 5]);
class(H)

Expected output:

ans = "tf"

Creating a second-order transfer function

H = tf([1 2], [1 3 2]);
H.Numerator
H.Denominator

Expected output:

H.Numerator = [1 2]
H.Denominator = [1 3 2]

Creating a discrete-time transfer function

H = tf(1, [1 -0.5], 0.1);
H.Variable
H.Ts

Expected output:

H.Variable = 'z'
H.Ts = 0.1

Creating a closed-loop model

s = tf('s');
G = 1/(s + 1);
T = feedback(2*G, 1);
dcgain(T)

Expected output:

ans = 0.6667

Selecting the polynomial variable

H = tf([1 0], [1 2 1], 'Variable', 'p');
H.Variable

Expected output:

H.Variable = 'p'

How RunMat validates tf

tf validates coefficient shapes, finite numeric values, supported variable names, sample-time constraints, and SISO arithmetic compatibility before constructing or combining host-side transfer-function objects. Unit and integration tests cover continuous and discrete constructors, variable shorthand, polynomial arithmetic, scalar division by transfer functions, row normalization, option parsing, and invalid denominator or matrix coefficient inputs.

• Implementation: `crates/runmat-runtime/src/builtins/control/tf.rs`

See Correctness & Trust for the full methodology and coverage table.

Using tf with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how tf changes the result.

FAQ

Related Control functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how tf is executed, line by line, in Rust.

• View the source for tf in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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