Polynomial Toolbox.
Version 3.0.19 10-May-2003
Global Structure
pinit - Initialize the Polynomial Toolbox
pver - Polynomial Toolbox version information
pversion - Polynomial Toolbox version number
gprops - Display/modify global properties
pformat - Modify output format
tolerance - Modify global relative tolerance
gensym - Modify global variable symbol
verbose - Modify global verbose level
checkpb - Check conflicts of Polynomial Toolbox
Polynomial(pol), Two-sided Polynomial(tsp) and Fraction Objects:
Left-denominator Fractions(ldf), Right-denominator Fractions(rdf),
Matrix-denominator Fractions(mdf) and Scalar-denominator
Fractions(sdf)
props - Display/modify properties of object
symbol - Display/modify variable symbol of object
userdata - Display/modify user data of object
pol - Create polynomial
lop - Create polynomial
tsp - Create two-sided polynomial
rdf - Create right-denominator fraction
ldf - Create left-denominator fraction
mdf - Create matrix-denominator fraction
sdf - Create scalar-denominator fraction
size - Size
length - Length
deg - Degree of pol or tsp
tdeg - Trailing degree of pol or tsp
coef - Coefficient of pol or tsp
lcoef - Leading coefficient of pol or tsp
tcoef - Trailing coefficient of pol or tsp
Special matrices
s - Basic variable (derivative operator)
p - Basic variable (derivative operator)
z - Basic variable (advance shift operator)
q - Basic variable (advance shift operator)
zi - Basic variable (delay shift operator)
d - Basic variable (delay shift operator)
v - Basic variable
mono - Monomial
Convertors
double - Convert to double (standard Matlab matrix)
pol - Convert to polynomial
tsp - Convert to two-sided polynomial
rdf - Convert to right-den fraction
ldf - Convert to left-den fraction
mdf - Convert to matrix-den fraction
sdf - Convert to scalar-den fraction
coldeg2pol - Convert column degree expanded form into the POL object.
pol2coldeg - Decomposition acording to column degrees
pol2rowdeg - Decomposition acording to row degrees
rowdeg2pol - Convert row degree expanded form into the POL object.
declass - Declass (convert to possible lower class)
defract - Remove denominator if possible
reverse - Reverse variable of fraction
abcd - Convert fraction to state space
abcde - Convert fraction to descriptor state space
ss - Convert fraction to Control Toolbox state space
dss - Convert fraction to Control Toolbox descriptor state space
tf - Convert fraction to Control Toolbox transfer function
zpk - Convert fraction to Control Toolbox zero-pole-gain
sym - Convert to Symbolic Toolbox
Overloaded operations
uplus - (+) Unary plus
uminus - (-) Unary minus
plus - (+) Add
minus - (-) Subtract
times - (.*) Element-wise multiply
mtimes - (*) Matrix multiply
power - (.^) Element-wise power
mpower - (^) Matrix power
rdivide - (./) Element-wise right divide
ldivide - (.\) Element-wise left divide
mrdivide - (/) Matrix right divide
mldivide - (\) Matrix left divide
kron - Kronecker tensor product
transpose - (.') Transpose
ctranspose - (') Conjugated transpose
eq - (==) Test if equal
ne - (~=) Test if unequal
display - Display
char - Convert to character string
horzcat - ([,]) Horizontal concatenate
vertcat - ([;]) Vertical concatenate
cat - Concatenate
subsref - Subscripted reference
subsasgn - Subscripted assignment
Overloaded functions
sum - Element-wise sum
prod - Element-wise product
inv - Inverse
pinv - Pseudoinverse
real - Real part
imag - Imaginary part
conj - Complex conjugate
diag - Diagonal matrix or diagonal
trace - Sum of diagonal elements
triu - Upper triangular part
tril - Lower triangular part
det - Determinant
adj - Adjoint of pol or tsp
isempty - Test if empty
isreal - Test if real
isfinite - Test if pol or tsp is finite
isinf - Test if pol or tsp is infinite
isnan - Test if pol or tsp is Not-a-Number
isprime - Test if pol matrix is left or right prime
rank - Rank
null - Nullspace of pol, tsp or fraction
norm - Norm
repmat - Replicate and tile
reshape - Change size
flipud - Flip rows up-down
fliplr - Flip columns left-right
rot90 - Rotate 90 degrees
roots - Roots
compan - Block companion matrix
lu - LU factorization of pol matrix
sylv - Sylvester matrix
Basic functions (other than overloaded)
pzer - Perform zeroing on a polynomial matrix
value - Value
mvalue - Matrix value
rdiv - Right divide with remainder
ldiv - Left divide with remainder
pgcd - Greatest common divisor of pols
gld - Greatest left divisor of pol matrices
grd - Greatest right divisor of pol matrices
plcm - Least common multiple of pols
llm - Least left multiple of pol matrices
lrm - Least right multiple of pol matrices
fact - Factor exctraction
deriv - Derivative
integral - Integral of pol or tsp
iscolred - Test for column reducedness of a polynomial matrix
isfullrank - Test if full rank
isrowred - Test for row reducedness of a polynomial matrix
issingular - Test if singula
isproper - Test if fraction is proper
evenpart - Even part of pol
oddpart - Odd part of pol
mirror - Mirror image of pol or tsp
pos - Positive part of tsp
neg - Negative part of tsp
npos - Nonpositive part of tsp
nneg - Nonnegative part of tsp
shift - Shift pol or tsp
scale - Scale pol
linvt - Linear transform of variable
coprime - Make fraction coprime
longldiv - Long left divide
longrdiv - Long right divide
laurent - Laurent series of fraction
polfit - Fit pol matrix element-by-element to data
polpart - Polynomial matrix part extraction
polyvalm - Evaluation of a polynomial in a matrix
Random functions
prand - Random pol
trand - Random tsp
rrand - Random rdf
lrand - Random ldf
mrand - Random mdf
srand - Random sdf
Advanced functions
charact - Characteristic vectors of pol matrix
complete - Complete to unimodular
ellsta - Ellipsoidal approximation of the stability domain
h2norm - H2 norm of fraction
hinfnorm - H-infinity norm of fraction
hurwitz - Create Hurwitz matrix of polynomial
inertia - Inertia of polynomial matrix
isminph - Test if minimum phase
isstable - Test if stable
isunimod - Test if unimodular
laplace - Inverse Laplace transform of fraction
minbasis - Minimal polynomial basis
moments - Moment of roots of a polynomial
jury - Jury matrix
kharit - Kharitonov polynomial
gram - Gramian of polynomial matrix fraction
Canonical and reduced forms
rowred - Row reduced form
colred - Column reduced form
diagred - Diagonal reduced form
pdg - Diagonal form
tri - Triangular or staircase form
hermite - Hermite form
smith - Smith form
echelon - Echelon form
bhf - Block Hessenberg form
bezout - Bezoutian matrix
hermfuji - Hermite-Fujiwara matrix
schurcohn - Schur-Cohn matrix
reduce - Make fraction reduced
Sampling period functions
samp - Sample continuous-time object
samph - Sample and zero order hold
samph1 - Sample and first order hold
samph2 - Sample and second order hold
resamp - Resample discrete-time object
resamph - Resample and zero order hold
resamph1 - Resample and first order hole
resamph2 - Resample and second order hold
unsamp - Unsample discrete-time object
unsamph - Un- sample and zero order hold
unsamph1 - Un- sample and first order hold
unsamph2 - Un- sample and second order hold
chsamp - Change sampling of discrete-time object
dilate - Dilate discrete-time object
Equation solvers
axb - Solution of AX = B
xab - Solution of XA = B
axbc - Solution of AXB = C
axby0 - Solution of AX + BY = 0
xayb0 - Solution of XA + YB = 0
axbyc - Solution of AX + BY = C
xaybc - Solution of XA + YB = C
axybc - Solution of AX + YB = C
axxab - Solution of A'X + X'A = B
xaaxb - Solution of XA' + AX' = B
axyab - Solution of AX' + Y'A = B
hqr - Hyperbolic QR factorization Q*A = R of a square matrix A
spf - Spectral factorization X'JX = B
spcof - Spectral co-factorization XJX' = B
gare - Generalized algebraic Riccati equation
Linear-matrix-inequality functions
lmianalysis - Analysis of stability of pol matrix
lmihinfnorm - H-inf norm of fraction
lmipolytope - Robust stability analysis of polytope
lmirank - Solve LMI for a matrix of specified rank
lmisimstab - Simultaneous stabilization of family of SISO systems
lmispf - Spectral factorization
lmispcof - Spectral co-factorization
Matrix pencil functions
clements - Conversion to Clements standard form
clements1 - Conversion to Clements standard form
pencan - Conversion to real Kronecker canonical form
plyap - Solution of the pencil equation A*X + Y*B = C
Numerical functions
cgivens1 - Calculates Givens rotation
qzord - Ordered QZ transformation
schurst - Ordered complex Schur decomposition of a matrix