nyquist — Compute or plot Nyquist frequency responses of SISO transfer-function models.

nyquist(sys) plots Nyquist responses for supported SISO tf models, and output forms return real, imaginary, and frequency vectors. It follows MATLAB-compatible call signatures for default or explicit frequency grids.

Syntax

nyquist(sys)
nyquist(sys, w)
re = nyquist(sys, w)
[re, im] = nyquist(sys, w)
[re, im, wout] = nyquist(sys)
[re, im, wout] = nyquist(sys, w)

• sys must currently be a SISO tf object.
• w must be a real vector of finite non-negative frequencies.
• re, im, and wout are returned as N x 1 column vectors.

How nyquist works

• Supports SISO tf objects created by tf(num, den) or tf(num, den, Ts).
• Continuous-time models are evaluated as H(j*w).
• Discrete-time models are evaluated on the unit circle as H(exp(j*w*Ts)).
• When w is omitted, continuous-time models use a deterministic logarithmic frequency grid based on transfer-function poles and zeros.
• When w is omitted, discrete-time models use a deterministic grid from zero to the Nyquist frequency pi/Ts.
• [re, im] = nyquist(sys, w) returns real and imaginary response column vectors.
• [re, im, wout] = nyquist(sys, w) returns three same-length column vectors.
• No-output calls plot the positive-frequency curve and mirror the negative-frequency curve for real-coefficient systems.
• Input/output delays and non-tf model classes raise clear diagnostics in this implementation.

GPU memory and residency

nyquist returns host-resident response vectors. It does not preserve gpuArray residency.

Examples

Compute response data at explicit frequencies

H = tf(1, [1 1]);
w = [0 1 2];
[re, im, wout] = nyquist(H, w);
fprintf("%.1f %.1f %.1f %.1f\n", re(1), re(2), im(2), wout(3));

Expected output:

1.0 0.5 -0.5 2.0

Plot a Nyquist diagram

H = tf(1, [1 2 1]);
nyquist(H);
fprintf("ok\n");

Expected output:

ok

Discrete-time frequency response

H = tf(1, [1 -0.5], 0.1);
[re, im] = nyquist(H, 0:0.5:5);
fprintf("%.1f %.1f\n", re(1), im(1));

Expected output:

2.0 0.0

How RunMat validates nyquist

nyquist validates object class, coefficient type and shape, delay properties, sample time, denominator singularities, and frequency-vector inputs before evaluating the transfer-function response. Tests cover continuous and discrete responses, multi-output shapes, plotting smoke, complex coefficients, VM dispatch, and representative diagnostics.

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

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

Using nyquist with coding agents

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

FAQ

Related Control functions

Open-source implementation

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

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

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