Control System Toolbox Function Reference

Functions by Category

LTI Models 

Function Name	Description
drss	Generate random discrete state-space model
dss	Create descriptor state-space model
filt	Create discrete filter with DSP convention
frd	Create a frequency response data (FRD) model
frdata	Retrieve data from an FRD model
get	Query LTI model properties
rss	Generate random continuous state-space model
set	Set LTI model properties
ss	Create state-space model
ssdata, dssdata	Retrieve state-space data
tf	Create transfer function
tfdata	Retrieve transfer function data
totaldelay	Provide the aggregate delay for an LTI model
zpk	Create zero-pole-gain model
zpkdata	Retrieve zero-pole-gain data

Model Characteristics

Function Name	Description
class	Display model type ('tf', 'zpk', 'ss', or 'frd')
hasdelay	Test true if LTI model has any type of delay
isa	Test true if LTI model is of specified type
isct	Test true for continuous-time models
isdt	Test true for discrete-time models
isempty	Test true for empty LTI models
isproper	Test true for proper LTI models
issiso	Test true for SISO models
ndims	Display the number of model/array dimensions
size	Display output/input/array dimensions

Model Conversion  

Function Name	Description
c2d	Convert from continuous- to discrete-time models
chgunits	Convert the units property for FRD models
d2c	Convert from discrete- to continuous-time models
d2d	Resample discrete-time models
delay2z	Convert delays in discrete-time models or FRD models
frd	Convert to a frequency response data model
pade	Compute the Padé approximation of delays
reshape	Change the shape of an LTI array
residue	Provide partial fraction expansion
ss	Convert to a state space model
tf	Convert to a transfer function model
zpk	Convert to a zero-pole-gain model

Model Order Reduction 

Function Name	Description
balreal	Calculate an I/O balanced realization
minreal	Calculate minimal realization or eliminate pole/zero pairs
modred	Delete states in I/O balanced realization
sminreal	Calculate structured model reduction

State-Space Realizations 

Function Name	Description
canon	Canonical state-space realizations
ctrb	Controllability matrix
ctrbf	Controllability staircase form
gram	Controllability and observability grammians
obsv	Observability matrix
obsvf	Observability staircase form
ss2ss	State coordinate transformation.
ssbal	Diagonal balancing of state-space realizations.

Model Dynamics

Function Name	Description
damp	Calculate natural frequency and damping
dcgain	Calculate low-frequency (DC) gain
covar	Calculate covariance of response to white noise
dsort	Sort discrete-time poles by magnitude
esort	Sort continuous-time poles by real part
norm	Calculate norms of LTI models ( and )
pole, eig	Calculate the poles of an LTI model
pzmap	Plot the pole/zero map of an LTI model
rlocus	Calculate and plot root locus
roots	Calculate roots of polynomial
sgrid,zgrid	Superimpose s- and z-plane grids for root locus or pole/zero maps
zero	Calculate zeros of an LTI model

Model Interconnections

Function Name	Description
append	Append models in a block diagonal configuration
augstate	Augment output by appending states
connect	Connect the subsystems of a block-diagonal model according to an interconnection scheme of your choice
feedback	Calculate the feedback connection of models
lft	Form the LFT interconnection (star product)
ord2	Generate second-order model
parallel	Create a generalized parallel connection
series	Create a generalized series connection
stack	Stack LTI models into a model array

Time Response 

Function Name	Description
gensig	Generate an input signal
impulse	Calculate and plot impulse response
initial	Calculate and plot initial condition response
lsim	Simulate response of LTI model to arbitrary inputs
ltiview	Open the LTI Viewer for linear response analysis
step	Calculate step response

LQG Design  

Function Name	Description
lqr	Calculate the LQ-optimal gain for continuous models
dlqr	Calculate the LQ-optimal gain for discrete models
lqry	Calculate the LQ-optimal gain with output weighting
lqrd	Calculate the discrete LQ gain for continuous models
kalman	Calculate the Kalman estimator
kalmd	Calculate the discrete Kalman estimator for continuous models
lqgreg	Form LQG regulator given LQ gain and Kalman filter

Equation Solvers 

Function Name	Description
care	Solve continuous-time algebraic Riccati equations
dare	Solve discrete-time algebraic Riccati equations
lyap	Solve continuous-time Lyapunov equations
dlyap	Solve discrete-time Lyapunov equations

Function Reference

Alphabetical List of Functions