MATLAB compatibility module

The control.matlab module contains a number of functions that emulate some of the functionality of MATLAB. The intent of these functions is to provide a simple interface to the python control systems library (python-control) for people who are familiar with the MATLAB Control Systems Toolbox (tm).

Creating linear models

tf(num, den[, dt])	Create a transfer function system.
ss(A, B, C, D[, dt])	Create a state space system.
frd(response, omega[, dt])	Construct a frequency response data (FRD) model.
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.

Utility functions and conversions

mag2db(mag)	Convert a magnitude to decibels (dB).
db2mag(db)	Convert a gain in decibels (dB) to a magnitude.
c2d(sysc, Ts[, method, alpha, ...])	Convert a continuous time system to discrete time by sampling.
ss2tf(sys)	Transform a state space system to a transfer function.
tf2ss(sys)	Transform a transfer function to a state space system.
tfdata(sys)	Return transfer function data objects for a system.

System interconnections

series(sys1, sys2, [..., sysn])	Return the series connection (sysn * ... *) sys2 * sys1.
parallel(sys1, sys2, [..., sysn])	Return the parallel connection sys1 + sys2 (+ ... + sysn).
feedback(sys1[, sys2, sign])	Feedback interconnection between two I/O systems.
negate(sys, **kwargs)	Return the negative of a system.
connect(*args)	Index-based interconnection of an LTI system.
append(sys1, sys2, [..., sysn])	Group LTI state space models by appending their inputs and outputs.

System gain and dynamics

dcgain(*args)	Compute the gain of the system in steady state.
pole(sys)	Compute system poles.
zero(sys)	Compute system zeros.
damp(sys[, doprint])	Compute natural frequencies, damping ratios, and poles of a system.
pzmap(sys[, grid, plot])	Plot a pole/zero map for a linear system.

Time-domain analysis

step(sys[, T, input, output, return_x])	Step response of a linear system.
impulse(sys[, T, input, output, return_x])	Impulse response of a linear system.
initial(sys[, T, X0, input, output, return_x])	Initial condition response of a linear system.
lsim(sys[, U, T, X0])	Simulate the output of a linear system.

Frequency-domain analysis

bode(syslist[, omega, dB, Hz, deg, ...])	Bode plot of the frequency response.
nyquist(syslist[, omega])	Nyquist plot of the frequency response.
nichols(data[, omega, grid, title, ax, label])	Nichols plot for a system.
margin(sysdata)	Calculate gain and phase margins and associated crossover frequencies.
freqresp(sysdata[, omega, omega_limits, ...])	Frequency response of an LTI system at multiple angular frequencies.
evalfr(sys, x[, squeeze])	Evaluate the transfer function of an LTI system for complex frequency x.

Compensator design

rlocus(sys[, gains, xlim, ylim, ...])	Root locus diagram.
sisotool(sys[, initial_gain, xlim_rlocus, ...])	Sisotool style collection of plots inspired by MATLAB's sisotool.
place(A, B, p)	Place closed loop eigenvalues.
lqr(A, B, Q, R[, N])	Linear quadratic regulator design.
dlqr(A, B, Q, R[, N])	Discrete-time linear quadratic regulator design.
lqe(A, G, C, QN, RN, [, NN])	Linear quadratic estimator design (Kalman filter) for continuous-time systems.
dlqe(A, G, C, QN, RN, [, N])	Linear quadratic estimator design (Kalman filter) for discrete-time systems.

State-space (SS) models

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.
ctrb(A, B[, t])	Controllabilty matrix.
obsv(A, C[, t])	Observability matrix.
gram(sys, type)	Gramian (controllability or observability).

Model simplification

minreal(sys[, tol, verbose])	Eliminate uncontrollable or unobservable states.
hsvd(sys)	Calculate the Hankel singular values.
balred(sys, orders[, method, alpha])	Balanced reduced order model of sys of a given order.
modred(sys, ELIM[, method])	Model reduction by state elimination.
era(YY, r)	Calculate ERA model of order r based on impulse-response data YY.
markov(Y, U, [, m])	Calculate the first m Markov parameters [D CB CAB ...] from data.

Time delays

pade(T[, n, numdeg])

Create a linear system that approximates a delay.

Matrix equation solvers and linear algebra

lyap(A, Q[, C, E, method])	Solves the continuous-time Lyapunov equation.
dlyap(A, Q[, C, E, method])	Solves the discrete-time Lyapunov equation.
care(A, B, Q[, R, S, E, stabilizing, ...])	Solves the continuous-time algebraic Riccati equation.
dare(A, B, Q, R[, S, E, stabilizing, ...])	Solves the discrete-time algebraic Riccati equation.

Additional functions

gangof4(*args[, omega, omega_limits, ...])	Plot the response of the "Gang of 4" transfer functions for a system.
unwrap(angle[, period])	Unwrap a phase angle to give a continuous curve.

Functions imported from other modules

linspace(start, stop[, num, endpoint, ...])	Return evenly spaced numbers over a specified interval.
logspace(start, stop[, num, endpoint, base, ...])	Return numbers spaced evenly on a log scale.
ss2zpk(A, B, C, D[, input])	State-space representation to zero-pole-gain representation.
tf2zpk(b, a)	Return zero, pole, gain (z, p, k) representation from a numerator, denominator representation of a linear filter.
zpk2ss(z, p, k)	Zero-pole-gain representation to state-space representation
zpk2tf(z, p, k)	Return polynomial transfer function representation from zeros and poles