Functions -- By Category (Function Reference)

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 Conversions

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

bandwidth
Calculate the bandwidth of SISO models

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

iopzmap
Plot the pole/zero map for I/O pairs of an LTI model

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 Responses

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

Time Delays

Function Name
Description

delay2z
Convert delays in discrete-time models or FRD models

pade
Compute the Padé approximation of delays

totaldelay
Provide the aggregate delay for an LTI model

Frequency Response

Function Name
Description

allmargin
Calculate all crossover frequencies and associated gain, phase, and delay margins

bode
Calculate and plot Bode response

bodemag
Calculate and plot Bode magnitude only

evalfr
Evaluate response at single complex frequency

freqresp
Evaluate frequency response for selected frequencies

interp
Interpolate FRD model between frequency points

linspace
Create a vector of evenly spaced frequencies

logspace
Create a vector of logarithmically spaced frequencies

ltiview
Open the LTI Viewer for linear response analysis

margin
Calculate gain and phase margins

ngrid
Superimpose grid lines on a Nichols plot

nichols
Calculate Nichols plot

nyquist
Calculate Nyquist plot

sigma
Calculate singular value plot

Pole Placement

Function Name
Description

acker
Calculate SISO pole placement design

place
Calculate MIMO pole placement design

estim
Form state estimator given estimator gain

reg
Form output-feedback compensator given state-feedback and estimator gains

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

Graphical User Interfaces for
Control System Analysis and Design

Function Name
Description

ltiview
Open the LTI Viewer for linear response analysis

sisotool
Open the SISO Design GUI

Functions -- Alphabetical List

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

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

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

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

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

Function Name	Description
`bandwidth`	Calculate the bandwidth of SISO models
`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
`iopzmap`	Plot the pole/zero map for I/O pairs of an LTI model
`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

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

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

Function Name	Description
`allmargin`	Calculate all crossover frequencies and associated gain, phase, and delay margins
`bode`	Calculate and plot Bode response
`bodemag`	Calculate and plot Bode magnitude only
`evalfr`	Evaluate response at single complex frequency
`freqresp`	Evaluate frequency response for selected frequencies
`interp`	Interpolate FRD model between frequency points
`linspace`	Create a vector of evenly spaced frequencies
`logspace`	Create a vector of logarithmically spaced frequencies
`ltiview`	Open the LTI Viewer for linear response analysis
`margin`	Calculate gain and phase margins
`ngrid`	Superimpose grid lines on a Nichols plot
`nichols`	Calculate Nichols plot
`nyquist`	Calculate Nyquist plot
`sigma`	Calculate singular value plot

Function Name	Description
`acker`	Calculate SISO pole placement design
`place`	Calculate MIMO pole placement design
`estim`	Form state estimator given estimator gain
`reg`	Form output-feedback compensator given state-feedback and estimator gains

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

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