Control System Toolbox

Functions -- Categorical List

General

ctrlpref	Set Control System Toolbox preferences
ltimodels	Detailed help on the various types of LTI models
ltiprops	Detailed help on available LTI model properties

Creating Linear Models

filt	Specify a digital filter
frd	Create a frequency-response data models
lti/set	Set/modify properties of LTI models
ss, dss	Create state-space models (continuous/discrete)
tf	Create transfer function models
zpk	Create zero/pole/gain models

Data Extraction

dssdata	Descriptor version of ssdata
frdata	Extract frequency-response data
lti/get	Access values of LTI model properties
ssdata	Extract state-space matrices
tfdata	Extract numerators and denominators
zpkdata	Extract zero/pole/gain data

Conversions

c2d	Convert from continuous- to discrete-time models
chunits	Convert the units property for FRD models
d2c	Convert from discrete- to continuous-time models
d2d	Test true for continuous-time models
frd	Convert to a frequency-response data model
ss	Convert to a state-space model
tf	Convert to a transfer function model
zpk	Convert to a zero/pole/gain model

System Interconnections

append	Group LTI systems by appending inputs and outputs
connect	Derive state-space models from block diagram descriptions
feedback	Feedback connections of two systems
lft	Generalized feedback interconnection (Redheffer star product)
parallel	Generalized parallel connection (see also overloaded +)
series	Generalized series connection (see also overloaded *)

System Gain and Dynamics

bandwidth	System bandwidth
dcgain	D.C. (low-frequency) gain
bandwidth	System bandwidth
damp	Natural frequency and damping of system poles
dsort	Norms of LTI systems
esort	Sort continuous poles by real part
iopzmap	Input/output pole/zero map
lti/norm	Norms of LTI systems
modsep	Region-based modal decomposition
pole, eig	System poles
pzmap	Pole/zero map
stabsep	Stable/unstable decomposition

Time Domain Analysis

covar	Covariance of response to white noise
gensig	Generate input signal for lsim
impulse	Impulse response
initial	Response of state-space system with given initial state
lsim	Response to arbitrary inputs
ltiview	Response analysis GUI (LTI Viewer)
step	Step response

Frequency Domain Analysis

allmargin	All crossover frequencies and related gain/phase margins
bode	Bode diagrams of the frequency response
bodemag	Bode magnitude diagram only
evalfr	Evaluate frequency response at given frequency
freqresp	Frequency response over a frequency grid
frd/interp	Interpolate frequency-esponse data
ltiview	Response analysis GUI (LTI Viewer)
margin	Gain and phase margins
nichols	Nichols plot
nyquist	Nyquist plot
sigma	Plot the pole/zero map of an LTI model

Classical Design

rlocus	Evans root locus
sisotool	SISO design GUI (root locus and loop-shaping techniques)

Pole Placement

acker	SISO pole placement
estim	Form estimator given estimator gain
place	MIMO pole placement
reg	Form regulator given state-feedback and estimator gain

LQR/LQG Design

augstate	Augment output by appending states
lqg	Single-step LQG design
lgr, dlqr	Linear-quadratic (LQ) state-feedback regulator
lqrd	Discrete LQ regulator for continuous plants
lqrreg	Form LQG regulator given LQ gain and Kalman estimator
lqgy	LQ regulator with output weighting
kalman	Kalman estimator
kalmand	Discrete Kalman estimator for continuous plants

State-Space Models

balreal	Grammian-based input/output balancing
canon	State-space canonical forms
ctrb	Controllability matrix
gram	Controllability and observability grammians
minreal	Minimal realization and pole/zero cancellation
modred	Model state reduction
margin	Calculate gain and phase margins
ngrid	Superimpose grid lines on a Nichols plot
nichols	Calculate Nichols plot
nyquist	Calculate Nyquist plot
obsv	Observability matrix
sminreal	Structurally minimal realization
ss2ss	State coordinate transformation
ssbal	Diagonal balancing of state-space realizations

Time Delays

delay2z	Replace delays by poles at z=0 or FRD phase shift
hasdelay	True for models with time delays
pade	Pade approximation of time delays
totaldelay	Total delay between each input/output pair

Model Dimensions and Characteristics

class	Model type ('tf', 'zpk', 'ss', or 'frd')
isct	True for continuous-time models
isdt	True for discrete-time models
isproper	True for proper models
issiso	True for single-input/single-output models
lti/ndims	Number of dimensions
lti/isempty	True for empty LTI models
reshape	Reshape array of linear models
size	Model sizes and order

Overloaded and Arithmetic Operators

+ and -	Add and subtract systems (parallel connection)
*	Multiply systems (series connection)
\	Left divide -- sys1\sys2 means inv(sys1)*sys2
/	Right divide -- sys1/sys2 means sys1*inv(sys2)
^	Powers of a given system
'	Pertransposition
.'	Transposition of input/output map
[..]	Concatenate models along inputs or outputs
stack	Stack models/arrays along some array dimension
lti/inv	Inverse of an LTI system
conj	Complex conjugation of model coefficients

Matrix Equation Solvers

bdschur	Block diagonalization of a square matrix
care, dare	Solve algebraic Riccati equations
gcare, gdare	Solve generalized algebraic Riccati equations
lyap, dlyap	Solve Lyapunov equations
lyapchol, dlyapschol	Square-root Lyapunov equations

Command-Line Plot Customization

bodeplot	Bode magnitude and phase plus plot handle
getoptions	Get the plot options handle
hsvplot	Hankel singular value plus plot handle
impulseplot	Impulse response plus plot handle
initialplot	Initial condition plus plot handle
iopzplot	Pole/zero maps for input/output pairs plus plot handle
lsimplot	Time response to arbitrary inputs plus plot handle
nicholsplot	Nichols plot plus plot handle
nyquistplot	Nyquist plus plot handle
pzplot	Pole/zero plus plot handle
rlocusplot	Root locus plus plot handle
setoptions	Set plot options
sigmaplot	Singular values of the frequency response plus plot handle
stepplot	Step response plus plot handle

Functions -- Alphabetical List

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