Function reference

The Python Control Systems Library control provides common functions for analyzing and designing feedback control systems.

Documentation is available in two forms: docstrings provided with the code, and the python-control users guide, available from the python-control homepage.

The docstring examples assume that the following import commands:

>>> import numpy as np
>>> import control as ct

Available subpackages

The main control package includes the most commpon functions used in analysis, design, and simulation of feedback control systems. Several additional subpackages are available that provide more specialized functionality:

  • flatsys: Differentially flat systems

  • matlab: MATLAB compatibility module

  • optimal: Optimization-based control

System creation

ss(A, B, C, D[, dt])

Create a state space system.

tf(num, den[, dt])

Create a transfer function system.

frd(d, w)

Construct a frequency response data model

zpk(zeros, poles, gain[, dt])

Create a transfer function from zeros, poles, gain.

rss([states, outputs, inputs, strictly_proper])

Create a stable random state space object.

drss([states, outputs, inputs, strictly_proper])

Create a stable, discrete-time, random state space system

NonlinearIOSystem(updfcn[, outfcn, params])

Nonlinear I/O system.

System interconnections

append(sys1, sys2, [..., sysn])

Group models by appending their inputs and outputs.

connect(sys, Q, inputv, outputv)

Index-based interconnection of an LTI system.

feedback(sys1[, sys2, sign])

Feedback interconnection between two I/O systems.

interconnect(syslist[, connections, ...])

Interconnect a set of input/output systems.


Return the negative of a system.

parallel(sys1, sys2, [..., sysn])

Return the parallel connection sys1 + sys2 (+ ... + sysn).

series(sys1, sys2, [..., sysn])

Return the series connection (sysn * ... *) sys2 * sys1.

Frequency domain plotting

bode_plot(syslist[, omega, plot, ...])

Bode plot for a system

describing_function_plot(H, F, A[, omega, ...])

Plot a Nyquist plot with a describing function for a nonlinear system.

nyquist_plot(syslist[, omega, plot, ...])

Nyquist plot for a system

gangof4_plot(P, C[, omega])

Plot the "Gang of 4" transfer functions for a system

nichols_plot(sys_list[, omega, grid])

Nichols plot for a system

nichols_grid([cl_mags, cl_phases, ...])

Nichols chart grid

Note: For plotting commands that create multiple axes on the same plot, the individual axes can be retrieved using the axes label (retrieved using the get_label method for the matplotliib axes object). The following labels are currently defined:

  • Bode plots: control-bode-magnitude, control-bode-phase

  • Gang of 4 plots: control-gangof4-s, control-gangof4-cs, control-gangof4-ps, control-gangof4-t

Time domain simulation

forced_response(sys[, T, U, X0, transpose, ...])

Compute the output of a linear system given the input.

impulse_response(sys[, T, X0, input, ...])

Compute the impulse response for a linear system.

initial_response(sys[, T, X0, input, ...])

Compute the initial condition response for a linear system.

input_output_response(sys, T[, U, X0, ...])

Compute the output response of a system to a given input.

step_response(sys[, T, X0, input, output, ...])

Compute the step response for a linear system.

phase_plot(odefun[, X, Y, scale, X0, T, ...])

Phase plot for 2D dynamical systems

Control system analysis


Return the zero-frequency (or DC) gain of the given system

describing_function(F, A[, num_points, ...])

Numerically compute the describing function of a nonlinear function

frequency_response(sys, omega[, squeeze])

Frequency response of an LTI system at multiple angular frequencies.


Return the input feedforward passivity (IFP) index for the system.


Return the output feedback passivity (OFP) index for the system.

ispassive(sys[, ofp_index, ifp_index])

Indicate if a linear time invariant (LTI) system is passive.


Calculate gain and phase margins and associated crossover frequencies

stability_margins(sysdata[, returnall, ...])

Calculate stability margins and associated crossover frequencies.

step_info(sysdata[, T, T_num, yfinal, ...])

Step response characteristics (Rise time, Settling Time, Peak and others).


Compute frequencies and gains at intersections with real axis in Nyquist plot.


Compute system poles.


Compute system zeros.

pzmap(sys[, plot, grid, title])

Plot a pole/zero map for a linear system.

root_locus(sys[, kvect, xlim, ylim, ...])

Root locus plot

sisotool(sys[, initial_gain, xlim_rlocus, ...])

Sisotool style collection of plots inspired by MATLAB's sisotool.

StateSpace.__call__(x[, squeeze, warn_infinite])

Evaluate system's frequency response at complex frequencies.

TransferFunction.__call__(x[, squeeze, ...])

Evaluate system's transfer function at complex frequencies.

Matrix computations

care(A, B, Q[, R, S, E, stabilizing, ...])

Solves the continuous-time algebraic Riccati equation

ctrb(A, B)

Controllabilty matrix

dare(A, B, Q, R[, S, E, stabilizing, ...])

Solves the discrete-time algebraic Riccati equation

dlyap(A, Q[, C, E, method])

Solves the discrete-time Lyapunov equation

lyap(A, Q[, C, E, method])

Solves the continuous-time Lyapunov equation

obsv(A, C)

Observability matrix

gram(sys, type)

Gramian (controllability or observability)

Control system synthesis

acker(A, B, poles)

Pole placement using Ackermann method

create_statefbk_iosystem(sys, gain[, ...])

Create an I/O system using a (full) state feedback controller

dlqr(A, B, Q, R[, N])

Discrete-time linear quadratic regulator design

h2syn(P, nmeas, ncon)

H_2 control synthesis for plant P.

hinfsyn(P, nmeas, ncon)

H_{inf} control synthesis for plant P.

lqr(A, B, Q, R[, N])

Linear quadratic regulator design

mixsyn(g[, w1, w2, w3])

Mixed-sensitivity H-infinity synthesis.

place(A, B, p)

Place closed loop eigenvalues

rootlocus_pid_designer(plant[, gain, sign, ...])

Manual PID controller design based on root locus using Sisotool

Model simplification tools

minreal(sys[, tol, verbose])

Eliminates uncontrollable or unobservable states in state-space models or cancelling pole-zero pairs in transfer functions.

balred(sys, orders[, method, alpha])

Balanced reduced order model of sys of a given order.


Calculate the Hankel singular values.

modred(sys, ELIM[, method])

Model reduction of sys by eliminating the states in ELIM using a given method.

era(YY, m, n, nin, nout, r)

Calculate an ERA model of order r based on the impulse-response data YY.

markov(Y, U[, m, transpose])

Calculate the first m Markov parameters [D CB CAB ...] from input U, output Y.

Nonlinear system support

describing_function(F, A[, num_points, ...])

Numerically compute the describing function of a nonlinear function

find_eqpt(sys, x0[, u0, y0, t, params, iu, ...])

Find the equilibrium point for an input/output system.

linearize(sys, xeq[, ueq, t, params])

Linearize an input/output system at a given state and input.

input_output_response(sys, T[, U, X0, ...])

Compute the output response of a system to a given input.

ss2io(*args, **kwargs)

Create an I/O system from a state space linear system.

summing_junction([inputs, output, ...])

Create a summing junction as an input/output system.

tf2io(sys[, ...])

Convert a transfer function into an I/O system

flatsys.point_to_point(sys, timepts[, x0, ...])

Compute trajectory between an initial and final conditions.

Stochastic system support

correlation(T, X[, Y, squeeze])

Compute the correlation of time signals.

create_estimator_iosystem(sys, QN, RN[, P0, ...])

Create an I/O system implementing a linear quadratic estimator

dlqe(A, G, C, QN, RN, [, N])

Linear quadratic estimator design (Kalman filter) for discrete-time systems.

lqe(A, G, C, QN, RN, [, NN])

Linear quadratic estimator design (Kalman filter) for continuous-time systems.

white_noise(T, Q[, dt])

Generate a white noise signal with specified intensity.

Utility functions and conversions

augw(g[, w1, w2, w3])

Augment plant for mixed sensitivity problem.

bdschur(a[, condmax, sort])

Block-diagonal Schur decomposition

canonical_form(xsys[, form])

Convert a system into canonical form

damp(sys[, doprint])

Compute natural frequencies, damping ratios, and poles of a system


Convert a gain in decibels (dB) to a magnitude

isctime(sys[, strict])

Check to see if a system is a continuous-time system

isdtime(sys[, strict])

Check to see if a system is a discrete time system

issiso(sys[, strict])

Check to see if a system is single input, single output


Return True if an object is a Linear Time Invariant (LTI) system, otherwise False


Convert a magnitude to decibels (dB)

modal_form(xsys[, condmax, sort])

Convert a system into modal canonical form


Convert a system into observable canonical form

pade(T[, n, numdeg])

Create a linear system that approximates a delay.


Convert a system into reachable canonical form


Reset configuration values to their default (initial) values.

sample_system(sysc, Ts[, method, alpha, ...])

Convert a continuous time system to discrete time by sampling

set_defaults(module, **keywords)

Set default values of parameters for a module.

similarity_transform(xsys, T[, timescale, ...])

Perform a similarity transformation, with option time rescaling.


Transform a state space system to a transfer function.


Return state space data objects for a system


Transform a transfer function to a state space system.


Return transfer function data objects for a system

timebase(sys[, strict])

Return the timebase for a system

timebaseEqual(sys1, sys2)

Check to see if two systems have the same timebase

unwrap(angle[, period])

Unwrap a phase angle to give a continuous curve


Use Feedback Systems (FBS) compatible settings.


Use MATLAB compatible configuration settings.

use_numpy_matrix([flag, warn])

Turn on/off use of Numpy matrix class for state space operations.