The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze
The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze
Resampling of polynomials in z ................................................................... 70 Dilating ........................................................................................................... 70 4 The Polynomial Matrix Editor ...................................................................... 72 Introduction .................................................................................................................. 72 Quick start .................................................................................................................... 72 Main window ................................................................................................................ 73 Main window buttons ..................................................................................... 73 Main window menus ....................................................................................... 73 Matrix Pad window ...................................................................................................... 74 Matrix Pad buttons .......................................................................................... 74 5 Polynomial matrix fractions .......................................................................... 76 Introduction .................................................................................................................. 76 Scalar-denominator-fractions ..................................................................................... 76 The sdf command ......................................................................................... 78 Comparison of fractions .................................................................................. 78 Coprime ........................................................................................................... 79 Reduce ............................................................................................................. 79 General properties cop, red ...................................................................... 79 Reverse ............................................................................................................ 80 Matrix-denominator-fractions .................................................................................... 81 The mdf command ......................................................................................... 82 Left and right polynomial matrix fractions ............................................................... 82 Right-denominator-fraction ............................................................................ 83 The rdf command ......................................................................................... 83 Left-denominator-fraction ............................................................................... 84 The ldf command ......................................................................................... 84 Mutual conversions of polynomial matrix fraction objects ...................................... 84 Computing with polynomial matrix fractions ........................................................... 86 Addition, subtraction and multiplication ........................................................ 86 Entrywise and matrix division ........................................................................ 88 Concatenation and working with submatrices ................................................ 89
Coefficients and coefficient matrices .............................................................. 90 Conjugation and transposition ........................................................................ 90 Polynomial matrix fractions, transfer functions and transfer function matrices .. 91 Transfer functions ........................................................................................... 91 Transfer function matrices .............................................................................. 92 Transfer functions from state space model and vice versa ............................. 93 Conversions of polynomial matrix fraction objects to and from other Matlab objects ............................................................................................................................ 95 Conversion to the Control System Toolbox Objects ...................................... 96 Conversion from the Control System Toolbox Objects ................................ 100 Conversion to the Symbolic Math Toolbox .................................................. 102 Conversion from the Symbolic Math Toolbox ............................................. 104 6 Conclusions .................................................................................................. 107
- Page 2 and 3: PolyX, Ltd E-mail: info@polyx.com S
- Page 4 and 5: Rank ..............................
- Page 8 and 9: 1 Quick Start Initialization Help E
- 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
Resampling of polynomials in z ................................................................... 70<br />
Dilating ........................................................................................................... 70<br />
4 <strong>The</strong> <strong>Polynomial</strong> Matrix Editor ...................................................................... 72<br />
Introduction .................................................................................................................. 72<br />
Quick start .................................................................................................................... 72<br />
Main window ................................................................................................................ 73<br />
Main window buttons ..................................................................................... 73<br />
Main window menus ....................................................................................... 73<br />
Matrix Pad window ...................................................................................................... 74<br />
Matrix Pad buttons .......................................................................................... 74<br />
5 <strong>Polynomial</strong> matrix fractions .......................................................................... 76<br />
Introduction .................................................................................................................. 76<br />
Scalar-denominator-fractions ..................................................................................... 76<br />
<strong>The</strong> sdf command ......................................................................................... 78<br />
Comparison of fractions .................................................................................. 78<br />
Coprime ........................................................................................................... 79<br />
Reduce ............................................................................................................. 79<br />
General properties cop, red ...................................................................... 79<br />
Reverse ............................................................................................................ 80<br />
Matrix-denominator-fractions .................................................................................... 81<br />
<strong>The</strong> mdf command ......................................................................................... 82<br />
Left and right polynomial matrix fractions ............................................................... 82<br />
Right-denominator-fraction ............................................................................ 83<br />
<strong>The</strong> rdf command ......................................................................................... 83<br />
Left-denominator-fraction ............................................................................... 84<br />
<strong>The</strong> ldf command ......................................................................................... 84<br />
Mutual conversions of polynomial matrix fraction objects ...................................... 84<br />
Computing with polynomial matrix fractions ........................................................... 86<br />
Addition, subtraction and multiplication ........................................................ 86<br />
Entrywise and matrix division ........................................................................ 88<br />
Concatenation and working with submatrices ................................................ 89
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