The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze

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1 Quick Start Initialization Help Every Polynomial Toolbox session starts with the initialization command pinit: pinit Polynomial Toolbox 3.0 initialized. To get started, type one of these: helpwin or poldesk. For product information, visit www.polyx.com or www.polyx.cz. This function creates global polynomial properties and assigns them to their default values. If you place this command in your startup.m file then the Polynomial Toolbox is automatically initialized. If you include lines such as path(path,'c:\Matlab\toolbox\polynomial') pinit in the startup.m file in the folder in which you start MATLAB then the toolbox is automatically included in the search path and initialized each time you start MATLAB. To see a list of all the commands and functions that are available type help polynomial To get help on any of the toolbox commands, such as axxab, type help axxab Some commands are overloaded, that is, there exist various commands of the same name for various objects. To get help on overloaded commands, you must also specify the object class of interest. So help pol/rank returns help on rank for pol objects (polynomial matrices) while help frac/rank returns help on rank for frac objects (polynomial fractions) etc.
How to define a polynomial matrix Basic objects of the Polynomial Toolbox are polynomial matrices. They may be looked at in two different ways. You may directly enter a polynomial matrix by typing its entries. Upon initialization the Polynomial Toolbox defines several indeterminate variables for polynomials and polynomial matrices. One of them is s. Thus, you can simply type P = [ 1+s s^2 2*s^3 1+2*s+s^2 ] to define the polynomial matrix 2 1 s s Ps () 3 2 2s12ss MATLAB returns P = 1 + s s^2 2s^3 1 + 2s + s^2 The Polynomial Toolbox displays polynomial matrices by default in this style. We may also render the polynomial matrix P as P() s 2s12ss 1 0 0 1 1 0 0 0 s 2 0 1 s 1 0 2 0 s 0 P 0 P 1 P 2 P 3 2 1s s 2 3 3 2 Polynomial matrices may be defined this way by typing P0 = [ 1 0; 0 1 ]; P1 = [ 1 0; 0 2 ]; P2 = [ 0 1; 0 1 ]; P3 = [ 0 0; 2 0 ]; P = pol([P0 P1 P2 P3],3) MATLAB again returns first P = 1 + s s^2 2s^3 1 + 2s + s^2 The display format may be changed to ―coefficient matrix style‖ by the command pformat coef
Page 2 and 3: PolyX, Ltd E-mail: info@polyx.com S
Page 4 and 5: Rank ..............................
Page 6 and 7: Resampling of polynomials in z ....
Page 10 and 11: Typing the name of the matrix P now
Page 12 and 13: Concatenation and working with subm
Page 14 and 15: ans = 1 0 0 1 s^2 s^3 1 - s 1 The c
Page 16 and 17: 2 Polynomial matrices Introduction
Page 18 and 19: Changing the default indeterminate
Page 20 and 21: Degrees and leading coefficients R
Page 22 and 23: 3 + 8s integral(F) ans = 2s + 1.5s^
Page 24 and 25: isunimod(U) ans = 1 Also the adjoin
Page 26 and 27: Bases and null spaces ans = 1 confi
Page 28 and 29: If P( s) is square then its roots a
Page 30 and 31: and simply type or or hurwitz(p) an
Page 32 and 33: Least common multiple If the only c
Page 34 and 35: Greatest common left divisor 0 -3 +
Page 36 and 37: Dual concepts M = lrm(A,B) M = 0.32
Page 38 and 39: 0 1 s^2 -s^3 -s 0 Reduced and canon
Page 40 and 41: Another triangular form Hermite for
Page 42 and 43: Invariant polynomials The entries a
Page 44 and 45: Bézout equations Matrix polynomial
Page 46 and 47: Factorizations returns X = Y = 0.25
Page 48 and 49: zpplot(1-s^2), grid zpplot(1+2*s^2+
Page 50 and 51: Spectral factorization zpplot(1+2*i
Page 52 and 53: Non-symmetric factorization or 1 0
Page 54 and 55: Transformation to Kronecker canonic
Page 56 and 57: common roots (including roots at in
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Derivatives and integrals ans = ans
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Conjugate transpose The operation o
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Zeros of symmetric twosided polynom
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For polynomial matrices with comple
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Non-symmetric equation Discrete-tim
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Resampling Sampling period Discrete
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Resampling of two-sided polynomials
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4 The Polynomial Matrix Editor Intr
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Matrix Pad window Matrix Pad button
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5 Polynomial matrix fractions Intro
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The sdf command Comparison of fract
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Reverse managed by switching the Po
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The mdf command -1 + s 0.5s ------
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Leftdenominatorfraction The ldf com
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Gmdf==Grdf ans = Grdf==Gldf ans = 1
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Entrywise and matrix division ans =
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Coefficients and coefficient matric
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Transfer function matrices or f2 =
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0 and then just types F=mdf(A,B,C,D
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Conversion to the Control System To
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y1 0 y2 0 Continuous-time model. Gt
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Conversion from the Control System
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Conversion to the Symbolic Math Too
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Conversion from the Symbolic Math T
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class(ans) ans = mdf 106
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A abcd · 65 addition · 10, 22, 57
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Q quick start · 8 quotient · 2 R
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The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze

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