Function Reference

Alphabetical List

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Uncertain Elements	Functions for building uncertain elements
Uncertain Matrices and Systems	Functions for building uncertain matrices and systems
Manipulation of Uncertain Models	Functions for transforming and analyzing uncertain models
Interconnection of Uncertain Models	Functions for connecting uncertain models
Model Order Reduction	Functions for generating low-order approximations to plant and controller models
Robustness and Worst-Case Analysis	Functions for characterizing system robustness and worst-case performance
Robustness Analysis for Parameter-Dependent Systems (P-Systems)	Functions for analyzing P-Systems
Controller Synthesis	H control design functions
m-Synthesis	Structured singular value control design functions
Sampled-Data Systems	Functions for analyzing sampled-data systems
Gain Scheduling	Functions for synethsizing gain-scheduled controllers
Frequency-Response Data (FRD) Models	Functions for operating on FRD models
Supporting Utilities	Additional functions for working with systems containing uncertain elements
LMIs	Functions for building and solving systems of Linear Matrix Inequalities
Simulink	Functions for using with Simulink models

Uncertain Elements

ucomplex	Create uncertain complex parameter
ucomplexm	Create uncertain complex matrix
udyn	Create unstructured uncertain dynamic system object
ultidyn	Create uncertain linear time-invariant object
ureal	Create uncertain real parameter

Uncertain Matrices and Systems

diag	Diagonalize vector of uncertain matrices and systems
randatom	Generate random uncertain atom objects
randumat	Create random uncertain matrix
randuss	Create random uncertain state-space model
ufrd	Create uncertain frequency response data (ufrd) object, or convert another model type to ufrd model
umat	Create uncertain matrix
uss	Specify uncertain state-space models or convert LTI model to uncertain state-space model

Manipulation of Uncertain Models

actual2normalized	Calculate normalized distance between nominal value and given value for uncertain atom
gridureal	Grid ureal parameters uniformly over range
isuncertain	True for uncertain systems
lftdata	Decompose uncertain object into fixed normalized and fixed uncertain parts
ltiarray2uss	Compute uncertain system bounding given LTI ss array
normalized2actual	Convert value for atom in normalized coordinates to corresponding actual value
repmat	Replicate and tile uncertain matrix
simplify	Simplify representation of uncertain object
squeeze	Remove singleton dimensions for umat objects
ucover	Fit an uncertain model to a set of LTI responses
uss/usample	Generate random samples of uncertain object
usubs	Substitute values for uncertain elements of uncertain objects
uss/ssbal	Scale state/uncertainty of uncertain system

Interconnection of Uncertain Models

iconnect	Create empty interconnection object
icsignal	Create icsignal object
imp2exp	Convert implicit linear relationship to explicit input-output relationship
stack	Construct array by stacking uncertain matrices, models, or arrays
sysic	Build interconnections of certain and uncertain matrices and systems

Model Order Reduction

balancmr	Balanced model truncation via square root method
bstmr	Balanced stochastic model truncation (BST) via Schur method
hankelmr	Hankel minimum degree approximation (MDA) without balancing
hankelsv	Compute Hankel singular values for stable/unstable or continuous/discrete system
imp2ss	Convert impulse response to approximate state-space realization
modreal	Modal form realization and projection
ncfmr	Balanced normalized coprime factor model reduction
reduce	Model order reduction using Hankel singular value based algorithms
schurmr	Balanced truncation via Schur method
slowfast	State-space slow-fast decomposition

Robustness and Worst-Case Analysis

cpmargin	Coprime stability margin of plant-controller feedback loop
gapmetric	Compute upper bounds on gap and nugap distances between two systems
loopmargin	Analyze feedback loop
loopsens	Analyze sensitivity of plant-controller feedback loop
mussv	Compute bounds on structured singular value (µ)
mussvextract	Extract muinfo structure returned by mussv
ncfmargin	Calculate normalized coprime stability margin of feedback loop
popov	Perform Popov robust stability test
robopt	Create options object for use with robuststab and robustperf
robustperf	Calculate robust performance margin of uncertain multivariable system
robuststab	Calculate robust stability margin of uncertain multivariable system
wcgain	Calculate bounds on worst-case gain of uncertain system
wcgopt	Create options object for use with wcgain, wcsens, and wcmargin
wcmargin	Calculate worst-case gain/phase margins for feedback loop
wcnorm	Calculate worst-case norm of uncertain matrix
wcsens	Calculate worst-case sensitivity and complementary sensitivity functions of feedback loop

Robustness Analysis for Parameter-Dependent Systems (P-Systems)

aff2pol	Convert affine parameter-dependent models to polytopic models
decay	Quadratic decay rate of polytopic or affine P-systems
ispsys	True for parameter-dependent systems
pdlstab	Assess robust stability of polytopic or parameter-dependent system
pdsimul	Time response of parameter-dependent system along parameter trajectory
polydec	Compute polytopic coordinates with respect to box corners
psinfo	Query characteristics of polytopic or parameter-dependent systems
psys	Specify polytopic or parameter-dependent linear system
pvec	Specify vector of uncertain or time-varying parameters
pvinfo	Query characteristics of parameter vector
quadperf	Compute quadratic H performance of polytopic or parameter-dependent system
quadstab	Assess quadratic stability of polytopic or affine parameter-dependent systems

Controller Synthesis

augw	Create augmented plant model for weighted mixed-sensitivity loop shaping design
h2hinfsyn	b Mixed H2/H synthesis with pole placement constraints
h2syn	H2 controller synthesis for LTI plant
hinfsyn	H optimal controller synthesis for LTI plant
loopsyn	H loop shaping controller synthesis
ltrsyn	LQG loop-transfer recovery controller synthesis
mkfilter	Generate Bessel, Butterworth, Chebyshev, or RC filter
mixsyn	H mixed-sensitivity controller synthesis
ncfsyn	H normalized coprime factor controller synthesis

µ-Synthesis

cmsclsyn	Constant matrix µ-synthesis
dksyn	Synthesis of robust controller via µ-synthesis D-K and D-G-K iteration
dkitopt	Create options object for use with dksyn
drawmag	Interactive mouse-based sketching and fitting tool
fitfrd	Fit D-scaling frequency response data with state-space model
fitmagfrd	Fit scaling magnitude data with stable, minimum-phase state-space model
genphase	Fit single-input/single-output magnitude data with real, rational, minimum-phase transfer function

Sampled-Data Systems

sdhinfnorm	Compute L2 norm of sampled-data system
sdhinfsyn	Sampled-data H controller synthesis
sdlsim	Time response of sampled-data feedback system

Gain Scheduling

hinfgs

Gain-scheduled H controller synthesis

Frequency-Response Data (FRD) Models

frd/loglog	Log-log scale plot of frd objects
frd/semilogx	Semilog scale plot of frd object
frd/rcond	Reciprocal condition estimator of frd object
frd/schur	Schur decomposition of frd object
frd/svd	Singular value decomposition of frd object

Supporting Utilities

bilin	Multivariable binlinear transform of frequency (s or z)
dmplot	Interpret disk gain and phase margins
mktito	Partition LTI system into two-input-two-output system
sectf	State-space sector bilinear transformation
skewdec	Create skew-symmetric matrix
symdec	Form symmetric matrix

LMIs

LMI Systems	Functions for specifying systems of LMIs
LMI Characteristics	Functions for extracting information about systems of LMIs
LMI Solvers	Functions for solving systems of LMIs
Validation of Results	Functions for analyzing and validating LMI optimization results
Modification of Systems of LMIs	Functions for altering systems of LMIs

LMI Systems

getlmis	Internal description of LMI system
lmiedit	Specify or display systems of LMIs as MATLAB expressions
lmiterm	Add new term to existing LMI
lmivar	Specify matrix variables in existing LMI system
newlmi	Add new LMI to LMI system
setlmis	Initialize description of LMI system

LMI Characteristics

dec2mat	Extract matrix variable value from vector of decision variables
decinfo	Describe how entries of matrix variable X relate to decision variables
decnbr	Number of decision variables in LMI system
lmiinfo	Information about existing system of LMIs
lminbr	Number of LMIs in LMI system
mat2dec	Extract vector of decision variables from matrix variable values
matnbr	Number of matrix variables in LMI system

LMI Solvers

defcx	Specify cTx objectives of mincx
feasp	Compute solution to given system of LMIs
gevp	Generalized eigenvalue minimization under LMI constraints
mincx	Minimize linear objective under LMI constraints

Validation of Results

evallmi	Evaluate LMI for given values of decision variables
showlmi	Left - and right-hand sides of evalauted LMI

Modification of Systems of LMIs

bilin	Multivariable binlinear transform of frequency (s or z)
dmplot	Interpret disk gain and phase margins
mktito	Partition LTI system into two-input-two-output system
sectf	State-space sector bilinear transformation
skewdec	Create skew-symmetric matrix
symdec	Form symmetric matrix

Simulink

ufind	Find all uncertain variables in Simulink model
ulinearize	Linearize Simulink model with Uncertain State Space block
usample	Generate random samples of uncertain variables

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Analyzing Stability Margins

Functions — Alphabetical List

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