Function Reference

Alphabetical List  Class Reference

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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 and Tuning H∞ control design functions µ-Synthesis Structured singular value control design functions Sampled-Data Systems Functions for analyzing sampled-data systems Gain Scheduling Functions for synthesizing 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

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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

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Uncertain Matrices and Systems

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

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Manipulation of Uncertain Models

actual2normalized	Transform actual values to normalized values
gridureal	Grid ureal parameters uniformly over their range
isuncertain	Check whether argument is uncertain class type
lftdata	Decompose uncertain objects into fixed normalized and fixed uncertain parts
normalized2actual	Convert value for atom in normalized coordinates to corresponding actual value
repmat	Replicate and tile array
simplify	Simplify representation of uncertain object
squeeze	Remove singleton dimensions for umat objects
usample	Generate random samples of uncertain variables
uss/ssbal	Scale state/uncertainty while preserving uncertain input/output map of uncertain system
usubs	Substitute given values for uncertain elements of uncertain objects

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Interconnection of Uncertain Models

iconnect	Create empty iconnect (interconnection) objects
icsignal	Create icsignal object of specified dimension
stack	Construct array by stacking uncertain matrices, models, or arrays
sysic	Build interconnections of certain and uncertain matrices and systems

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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	System realization via Hankel singular value decomposition
modreal	Modal form realization and projection
ncfmr	Balanced model truncation for normalized coprime factors
reduce	Simplified access to Hankel singular value based model reduction functions
schurmr	Balanced model truncation via Schur method
slowfast	Slow and fast modes decomposition

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Robustness and Worst-Case Analysis

cpmargin	Coprime stability margin of plant-controller feedback loop
gapmetric	Compute upper bounds on Vinnicombe gap and nugap distances between two systems
loopmargin	Stability margin analysis of LTI and Simulink feedback loops
loopsens	Sensitivity functions 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 plant-controller feedback loop
popov	Perform Popov robust stability test
robustperf	Robust performance margin of uncertain multivariable system
robuststab	Calculate robust stability margins of uncertain multivariable system
wcgain	Calculate bounds on worst-case gain of uncertain system
wcgainplot	Worst-case gain analysis for uncertain systems
wcmargin	Worst-case disk stability margins of uncertain feedback loops
wcnorm	Worst-case norm of uncertain matrix
wcsens	Calculate worst-case sensitivity and complementary sensitivity functions of plant-controller feedback loop

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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 given parameter trajectory
polydec	Compute polytopic coordinates with respect to box corners
psinfo	Inquire about polytopic or parameter-dependent systems created with psys
pvec	Specify range and rate of variation of uncertain or time-varying parameters
pvinfo	Describe parameter vector specified with pvec
quadperf	Compute quadratic H∞ performance of polytopic or parameter-dependent system
quadstab	Quadratic stability of polytopic or affine parameter-dependent systems

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Controller Synthesis and Tuning

augw	State-space or transfer function plant augmentation for use in weighted mixed-sensitivity H∞ and H2 loopshaping design
h2hinfsyn	Mixed H2/H∞ synthesis with pole placement constraints
h2syn	H2 control synthesis for LTI plant
hinfstruct	H∞ tuning of fixed-structure controllers
hinfsyn	Compute H∞ optimal controller for LTI plant
loopsyn	H∞ optimal controller synthesis for LTI plant
looptune	Tune MIMO control systems
loopview	Graphically analyze MIMO feedback loops
ltrsyn	LQG loop transfer-function recovery (LTR) control synthesis
mixsyn	H∞ mixed-sensitivity synthesis method for robust control loopshaping design
mkfilter	Generate Bessel, Butterworth, Chebyshev, or RC filter
ncfsyn	Loop shaping design using Glover-McFarlane method

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µ-Synthesis

cmsclsyn	Approximately solve constant-matrix, upper bound µ-synthesis problem
dkitopt	Create options object for use with dksyn
dksyn	Robust controller design using µ-synthesis
drawmag	Mouse-based tool for sketching and fitting
fitfrd	Fit frequency response data with state-space model
fitmagfrd	Fit frequency response magnitude data with minimum-phase state-space model using log-Chebychev magnitude design
genphase	Fit single-input/single-output magnitude data with real, rational, minimum-phase transfer function

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Sampled-Data Systems

sdhinfnorm	Compute L2 norm of continuous-time system in feedback with discrete-time system
sdhinfsyn	Compute H∞ controller for sampled-data system
sdlsim	Time response of sampled-data feedback system

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Gain Scheduling

hinfgs

Synthesis of gain-scheduled H∞ controllers

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Frequency-Response Data (FRD) Models

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

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Supporting Utilities

bilin	Multivariable bilinear 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	Form skew-symmetric matrix
symdec	Form symmetric matrix

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LMIs

LMI Systems LMI Characteristics LMI Solvers Validation of Results Modification of Systems of LMIs

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LMI Systems

getlmis	Internal description of LMI system
lmiedit	Specify or display systems of LMIs as MATLAB expressions
lmiterm	Specify term content of LMIs
lmivar	Specify matrix variables in LMI problem
newlmi	Attach identifying tag to LMIs
setlmis	Initialize description of LMI system

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LMI Characteristics

dec2mat	Given values of decision variables, derive corresponding values of matrix variables
decinfo	Describe how entries of matrix variable X relate to decision variables
decnbr	Total number of decision variables in system of LMIs
lmiinfo	Information about variables and term content of LMIs
lminbr	Return number of LMIs in LMI system
mat2dec	Extract vector of decision variables from matrix variable values
matnbr	Number of matrix variables in system of LMIs

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LMI Solvers

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

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Validation of Results

evallmi	Given particular instance of decision variables, evaluate all variable terms in system of LMIs
showlmi	Return left and right sides of LMI after evaluation of all variable terms

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Modification of Systems of LMIs

bilin	Multivariable bilinear 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	Form skew-symmetric matrix
symdec	Form symmetric matrix

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Simulink

ufind	Find uncertain variables in Simulink model
ulinearize	Linearize Simulink model with Uncertain State Space block

Class Reference

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