`feedback` — Form SISO feedback interconnections for transfer-function models.

feedback(sys1, sys2) returns the closed-loop SISO transfer function for negative feedback. sys2 may be another compatible tf object or a scalar gain.

Syntax

sys = feedback(sys1)
sys = feedback(sys1, sys2)
sys = feedback(sys1, sys2, sign)

Inputs

Name	Type	Required	Default	Description
`sys1`	`Any`	Yes	—	Forward-path SISO transfer-function model.
`sys2`	`Any`	No	`1`	Feedback-path SISO transfer function or scalar gain.
`sign`	`NumericScalar`	No	`-1`	-1 for negative feedback or +1 for positive feedback.

Returns

Name	Type	Description
`sys`	`Any`	Closed-loop SISO transfer-function object.

Errors

Identifier	When	Message
`RunMat:feedback:InvalidArgument`	Inputs do not match supported feedback invocation forms.	`feedback: invalid argument`
`RunMat:feedback:InvalidModel`	Input systems are not supported SISO transfer-function models.	`feedback: invalid model`
`RunMat:feedback:InvalidSign`	Feedback sign is not -1 or +1.	`feedback: sign must be -1 or +1`
`RunMat:feedback:UnsupportedModel`	A supported-looking model uses unsupported delays or incompatible sample times.	`feedback: unsupported model`
`RunMat:feedback:Internal`	Closed-loop transfer-function assembly failed.	`feedback: internal error`

How `feedback` works

Supports real or complex SISO tf objects represented by numerator and denominator coefficient vectors.
feedback(sys1) uses unity negative feedback.
feedback(sys1, sys2) computes sys1/(1 + sys1*sys2).
feedback(sys1, sys2, +1) computes positive feedback as sys1/(1 - sys1*sys2).
Scalar gains are promoted to constant transfer functions using the other operand's variable and sample time.
Input systems must have compatible sample times.
Nonzero input or output delays are rejected with a clear unsupported-model diagnostic.

GPU memory and residency

feedback returns a host-side tf object. It does not preserve gpuArray residency.

Examples

Unity negative feedback

s = tf('s');
G = 2/(s + 3);
T = feedback(G, 1);
T.Denominator

Expected output:

ans = [1 5]

Positive feedback

G = tf(2, [1 3]);
T = feedback(G, 1, +1);
T.Denominator

Expected output:

ans = [1 1]

How RunMat validates `feedback`

feedback validates argument count, feedback sign, sample-time compatibility, zero-delay support, and transfer-function model shape. Tests cover unity negative feedback, positive feedback, scalar gains, and VM workflows using tf('s').

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

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

Using `feedback` with coding agents

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

Run a small feedback example, explain the result, then change one input and compare the output.

FAQ

Does feedback support MIMO systems?⌄

Not yet. This implementation supports SISO transfer-function objects and scalar gains.

Does it support state-space models?⌄

Not yet. The current model-family support is SISO tf.

db · dcgain · impulse · isstable · nyquist · pole · ss · step · stepinfo · tf

Open-source implementation

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

View the source for feedback 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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feedback — Form SISO feedback interconnections for transfer-function models.