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Robust Control Toolbox Functions

Alphabetical List By Category

Uncertain System Representation

Uncertain Models

urealCreate uncertain real parameter
umatCreate uncertain matrix
ucomplexCreate uncertain complex parameter
ucomplexmCreate uncertain complex matrix
ultidynCreate uncertain linear time-invariant object
ussSpecify uncertain state-space models or convert LTI model to uncertain state-space model
ufrdUncertain frequency response data model
randatomGenerate random uncertain atom objects
randumatGenerate random uncertain umat objects
randussGenerate stable, random uss objects
getNominalNominal value of uncertain model
actual2normalizedTransform actual values to normalized values
normalized2actualConvert value for atom in normalized coordinates to corresponding actual value
simplifySimplify representation of uncertain object
isuncertainCheck whether argument is uncertain class type
lftdataDecompose uncertain objects into fixed certain and normalized uncertain parts
ltiarray2ussCompute uncertain system bounding given LTI ss array
ucoverFit an uncertain model to set of LTI responses

Uncertain Models in Simulink

ulinearizeLinearize Simulink model with Uncertain State Space block

Uncertain System Analysis

Nominal Performance Analysis

loopmarginStability margin analysis of LTI and Simulink feedback loops
dmplotInterpret disk gain and phase margins
gapmetricCompute upper bounds on Vinnicombe gap and nugap distances between two systems
loopsensSensitivity functions of plant-controller feedback loop
ncfmarginCalculate normalized coprime stability margin of plant-controller feedback loop
sdhinfnormCompute L2 norm of continuous-time system in feedback with discrete-time system
sdlsimTime response of sampled-data feedback system

Robustness and Worst-Case Analysis

robstabRobust stability of uncertain system
robgainRobust performance of uncertain system
robOptionsOption set for robustness analysis
wcgainWorst-case gain of uncertain system
wcsigmaPlot worst-case gain of uncertain system
wcnormWorst-case norm of uncertain matrix
wcsensCalculate worst-case sensitivity and complementary sensitivity functions of plant-controller feedback loop
wcmarginWorst-case disk stability margins of uncertain feedback loops
wcOptionsOption set for worst-case analysis
mussvCompute bounds on structured singular value (µ)
mussvextractExtract muinfo structure returned by mussv

Monte Carlo Analysis

uss/usampleGenerate random samples of uncertain or generalized model
usampleGenerate random samples of uncertain variables in a Simulink model
rsampleBlockRandomly sample Control Design blocks in generalized model
usubsSubstitute given values for uncertain elements of uncertain objects
gridurealGrid ureal parameters uniformly over their range
complexifyReplace ureal atoms by summations of ureal and ucomplex (or ultidyn) atoms

Uncertainty Analysis with Simulink Models

ufindFind uncertain variables in Simulink model
ulinearizeLinearize Simulink model with Uncertain State Space block
usampleGenerate random samples of uncertain variables in a Simulink model
loopmarginStability margin analysis of LTI and Simulink feedback loops

Robust Controllers

Robust Tuning

urealCreate uncertain real parameter
systuneTune fixed-structure control systems modeled in MATLAB
slTunerInterface for control system tuning of Simulink models
systune (slTuner)Tune control system parameters in Simulink using slTuner interface

H-Infinity Synthesis

hinfstructH∞ tuning of fixed-structure controllers
hinfstructOptionsSet options for hinfstruct
hinfsynCompute H∞ optimal controller for LTI plant
h2synH2 control synthesis for LTI plant
sdhinfsynCompute H∞ controller for sampled-data system
h2hinfsynMixed H2/H∞ synthesis with regional pole placement constraints
hinfnormH∞ norm of dynamic system
augwState-space or transfer function plant augmentation for use in weighted mixed-sensitivity H∞ and H2 loopshaping design
mkfilterGenerate Bessel, Butterworth, Chebyshev, or RC filter
makeweightFirst-order weighting function with specified DC gain, crossover frequency, and high-frequency gain

Loop-Shaping Synthesis

loopsynH∞ optimal controller synthesis for LTI plant
mixsynH∞ mixed-sensitivity synthesis method for robust control loopshaping design
ncfsynLoop shaping design using Glover-McFarlane method

Mu Synthesis

dksynRobust controller design using µ-synthesis
dksynperfRobust H∞ performance optimized by dksyn
dksynOptionsSet options for dksyn
cmsclsynApproximately solve constant-matrix, upper bound µ-synthesis problem
drawmagMouse-based tool for sketching and fitting
fitfrdFit frequency response data with state-space model
fitmagfrdFit frequency response magnitude data with minimum-phase state-space model using log-Chebyshev magnitude design
genphaseFit single-input/single-output magnitude data with real, rational, minimum-phase transfer function

Model Simplification

reduceSimplified access to Hankel singular value based model reduction functions
balancmrBalanced model truncation via square root method
bstmrBalanced stochastic model truncation (BST) via Schur method
hankelmrHankel minimum degree approximation (MDA) without balancing
hankelsvCompute Hankel singular values for stable/unstable or continuous/discrete system
modrealModal form realization and projection
ncfmrBalanced model truncation for normalized coprime factors
schurmrBalanced model truncation via Schur method
dcgainmrReduced order model
slowfastSlow and fast modes decomposition

Linear Matrix Inequalities

LMI Solvers

getlmisInternal description of LMI system
lmieditSpecify or display systems of LMIs as MATLAB expressions
lmitermSpecify term content of LMIs
lmivarSpecify matrix variables in LMI problem
newlmiAttach identifying tag to LMIs
setlmisInitialize description of LMI system
dellmiRemove LMI from system of LMIs
delmvarRemove one matrix variable from LMI problem
setmvarInstantiate matrix variable and evaluate all LMI terms involving this matrix variable
dec2matGiven values of decision variables, derive corresponding values of matrix variables
decinfoDescribe how entries of matrix variable X relate to decision variables
decnbrTotal number of decision variables in system of LMIs
lmiinfoInformation about variables and term content of LMIs
lminbrReturn number of LMIs in LMI system
mat2decExtract vector of decision variables from matrix variable values
matnbrNumber of matrix variables in system of LMIs
defcxHelp specify cTx objectives for mincx solver
feaspCompute solution to given system of LMIs
gevpGeneralized eigenvalue minimization under LMI constraints
mincxMinimize linear objective under LMI constraints
evallmiGiven particular instance of decision variables, evaluate all variable terms in system of LMIs
showlmiReturn left and right sides of LMI after evaluation of all variable terms

Parameter-Dependent Systems

aff2polConvert affine parameter-dependent models to polytopic models
decayQuadratic decay rate of polytopic or affine P-systems
ispsysTrue for parameter-dependent systems
pdlstabAssess robust stability of polytopic or parameter-dependent system
pdsimulTime response of parameter-dependent system along given parameter trajectory
polydecCompute polytopic coordinates with respect to box corners
psinfoInquire about polytopic or parameter-dependent systems created with psys
psysSpecify polytopic or parameter-dependent linear systems
pvecSpecify range and rate of variation of uncertain or time-varying parameters
pvinfoDescribe parameter vector specified with pvec
quadperfCompute quadratic H∞ performance of polytopic or parameter-dependent system
quadstabQuadratic stability of polytopic or affine parameter-dependent systems

LMI Controller Synthesis

hinfgsSynthesis of gain-scheduled H∞ controllers
hinfsynCompute H∞ optimal controller for LTI plant
h2hinfsynMixed H2/H∞ synthesis with regional pole placement constraints
msfsynMulti-model/multi-objective state-feedback synthesis
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