LFRT version 1.3 for Matlab: functions

TOOLBOXES TUTORIAL

Help files

addobs abcd2lfr approxlfr bfb2lfr bnds2lfr clfrs conv-2lfr
data2lfr data2sym depl2lfr deps2lfr difflfr distlfr eig_fb
fb_sched fldown flup fullblk fullblkb kron lfr2abcd
lfr2bsys lfr2data lfr2lmim lfr2lmip lfr2mua lfr2ss lfr2swp
lfrs lfrtol lfrview lyap makegrid min_max minlfr
minlfr1 ndh2lfr ndv2lfr normlfr ns_rad null ordelta
obs2klfr ob_sched plotlfr pluglfr ppole pqrdelta reduclfr
reorder rlfr smlk2lfr starplfr sym2lfr symbplot symtreed
udistlfr wp_rad

Lists of LFRT function ordered by topics


The following functions of the directory @lfr are implicitly called: ctranspose, horzcat, minus, mrdivide, mtimes, mpower, plus, uminus, vertcat. These functions permit the user to manipulate lfr-objects like matrices. Other functions of @lfr that can be explicitly called:
lfr Core function for lfr generation
size Overloaded function for lfr-objects
eig Overloaded function for lfr-objects
eig_fb Overloaded function for lfr-objects
feedback Overloaded function for lfr-objects
inv Overloaded function for lfr-objects
kron Overloaded function for lfr-objects
lyap Overloaded function for lfr-objects
null Overloaded function for lfr-objects
subsref For retrieving data in an lfr-object like: sys.a, sys.b, sys.c, sys.d, sys.e but also elements (e.g., sys(1:3,:)

lfr-object generation
convert2lfr Converts matrices, ss-objects, lti-systems
lfrs Shortcut for 1-by-1 real lfr generation
clfrs Shortcut for 1-by-1 complex lfr generation
rlfr Generates random lfr-objects
fullblk Generation of full real/complex blocks
fullblkb Similar but backward
bnds2lfr From min/max bounds to lfr
abcd2lfr From system matrix lfr to input/output lfr
lfr2abcd From input/output lfr to system matrix lfr
ndv2lfr From N*D^-1 to lfr
ndh2lfr From D^-1*N to lfr

lfr realization
depl2lfr Morton technique: linear dependency
deps2lfr Morton technique adapted to symbolic dependency
sym2lfr Symbolic expression converted to lfr
symtreed Similar, but uses tree decomposition
smlk2lfr From Simulink to lfr

Parameter gridding
data2lfr Interpolation on an lfr basis
data2sym Interpolation on a symbolic basis
lfr2data Evaluates an lfr-object on a gridding
symbplot Colors and symbols depending on parameter values
makegrid Defines a parameter gridding
lfr2ss Transforms an lfr-object to an array of ss-objects
plotlfr Plots values of an lfr-object on a gridding
ppole Plots poles of a dynamic lfr-object on a gridding
lfrview Plots several responses of a dynamic lfr-object on a gridding

Order reduction
minlfr Reduction based on n-D Kalman decomposition
minlfr1 Sequencial 1-D lfr odred reduction
symtreed Tree decomposition for low order modelling
udistlfr Validates approximations
reduclfr minlfr used for approximation
approxlfr Gramian-based approximation
lfrtol For systematic order reduction (addition, multiplication, concatenation)

Distances
distlfr Computes the distance between two lfrs
udistlfr Computes an upperbound of the distance between two lfrs
min_max Minimum and maximum values of a 1-by-1 lfr

Manipulation of the delta-block
normlfr Normalizes uncertainty variations
ordelta Re-ordering the uncertainties in the delta-block
pqrdelta Delta_1 = P Delta_2 Q + R replaced by Delta_2
reorder Re-ordering the uncertainties in the delta-block
pluglfr Elaborated star product

Feedback
fldown Closes the feedback loop and removes input/outputs
flup Closes (partially) the delta-loop
pluglfr Elaborated star product
starplfr Star product for lfr-objects

Mu analysis
lfr2lmim Adaptation to the LMI-Control Toolbox (mubnd)
lfr2lmip Adaptation to the LMI-Control Toolbox (mustab)
lfr2mua Adaptation to the mu-Analysis and Control Toolbox
lfr2swp Adaptation to muan/swplmu for lower bound computation
ns_rad Non-singularity radius of non-dynamic lfr-object
wp_rad Well-posedness radius of non-dynamic lfr-object

Gain scheduling 1
lfr2bsys Transforms an ss-object into a bigger one so that gain scheduling becomes a robust control design problem.
bfb2lfr Back transformation of the robust gain (big system) to a scheduled gain (original system).

Gain scheduling 2
fb_sched Scheduled/multi-model eigenstructure assignment.
ob_sched Scheduled observer design
addobs Add a scheduled observer to a system (for use of fb_sched)
obs2klfr Transforms an obsever-based feedback to an ordinary scheduled feedback.

General functions
help1 Help message without illustrative example
help2 Illustrative example
lfrtdemo Graphic interface
disptext Displays text

Required Toolboxes:

Control Toolbox for most functions
Symbolic Toolbox: deps2lfr, data2sym, sym2lfr, symtreed
LMI Toolbox: lfr2lmim, lfr2lmip
Mu Analysis and Control Toolbox: lfr2mua, min_max, reduclfr, ns_rad, wp_rad
Simulink: smlk2lfr

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