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280 <strong>GNU</strong> <strong>Octave</strong>[pol, zer, k] = ss2zp (a, b, c, d)Function FileConverts a state space representation to a set of poles and zeros; k is a gain associatedwith the zeros.Used internally in system data structure format manipulations.starp (P, K, ny, nu)Redheffer star product or upper/lower LFT, respectively.Function File+-------+--------->| |--------->| P |+--->| |---+ ny| +-------+ |+-------------------+| |+----------------+ || || +-------+ |+--->| |------+ nu| K |--------->| |--------->+-------+If ny and nu “consume” all inputs and outputs of K then the result is a lower fractionaltransformation. If ny and nu “consume” all inputs and outputs of P then the resultis an upper fractional transformation.ny and/or nu may be negative (i.e. negative feedback).[a, b, c, d] = tf2ss (num, den)Conversion from tranfer function to state-space. The state space system:Function Fileis obtained from a transfer function:ẋ = Ax + Buy = Cx + DuG(s) = num(s)den(s)The vector den must contain only one row, whereas the vector num may contain asmany rows as there are outputs y of the system. The state space system matricesobtained from this function will be in controllable canonical form as described inModern Control Theory, (Brogan, 1991).[zer, pol, k] = tf2zp (num, den)Converts transfer functions to poles-and-zero representations.Returns the zeros and poles of the siso system defined by num/den.associated with the system zeros.Function Filek is a gain
Chapter 29: Control Theory 281[a, b, c, d] = zp2ss (zer, pol, k)Conversion from zero / pole to state space.InputsFunction FilezerpolkVectors of (possibly) complex poles and zeros of a transfer function. Complexvalues must come in conjugate pairs (i.e., x+jy in zer means thatx − jy is also in zer). The number of zeros must not exceed the numberof poles.Real scalar (leading coefficient).OutputsabcdThe state space system, in the form:ẋ = Ax + Buy = Cx + Du[num, den] = zp2tf (zer, pol, k)Converts zeros / poles to a transfer function.InputsFunction FilezerpolkVectors of (possibly complex) poles and zeros of a transfer function. Complexvalues must appear in conjugate pairs.Real scalar (leading coefficient).
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GNU OctaveA high-level interactive
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iTable of ContentsPreface . . . . .
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10 Expressions . . . . . . . . . .
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19 Arithmetic . . . . . . . . . . .
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Appendix A Tips and Standards . . .
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Preface 1PrefaceOctave was original
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Preface 3• Tony Richardson richar
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Chapter 1: A Brief Introduction to
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Chapter 2: Getting Started 132 Gett
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Chapter 2: Getting Started 15argvBu
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Chapter 2: Getting Started 17helpCo
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Chapter 2: Getting Started 19clc ()
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Chapter 2: Getting Started 21C-rC-s
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Chapter 2: Getting Started 23‘\h
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Chapter 2: Getting Started 25Anothe
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Chapter 2: Getting Started 27usage:
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Chapter 3: Data Types 293 Data Type
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Chapter 3: Data Types 31size (a, n)
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Chapter 4: Numeric Data Types 334 N
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Chapter 4: Numeric Data Types 35war
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Chapter 4: Numeric Data Types 37Emp
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Chapter 5: Strings 395 StringsA str
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Chapter 5: Strings 41string fill ch
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Chapter 5: Strings 435.3 String Con
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Chapter 5: Strings 45toupper (s)Bui
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Chapter 6: Data Structures 476 Data
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Chapter 6: Data Structures 49octave
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Chapter 7: Containers 517 Container
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Chapter 8: I/O Streams 538 I/O Stre
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Chapter 9: Variables 559 VariablesV
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Chapter 9: Variables 57persistent p
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Chapter 9: Variables 59exist (name,
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Chapter 9: Variables 61default_save
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Chapter 9: Variables 63warn_divide_
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Chapter 10: Expressions 6510 Expres
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Chapter 10: Expressions 67sqrt (arg
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Chapter 10: Expressions 69x - ySubt
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Chapter 10: Expressions 7110.5.1 El
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Chapter 10: Expressions 73z = 1Afte
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Chapter 10: Expressions 75++x--xThi
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Chapter 11: Evaluation 7711 Evaluat
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Chapter 12: Statements 7912 Stateme
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Chapter 12: Statements 81warn assig
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Chapter 12: Statements 83while (con
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Chapter 12: Statements 85for [ val,
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Chapter 12: Statements 87# print el
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Chapter 12: Statements 89For contin
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Chapter 13: Functions and Script Fi
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Chapter 14: Error Handling 10514 Er
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Chapter 15: Debugging 10715 Debuggi
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Chapter 16: Input and Output 10916
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Chapter 16: Input and Output 111for
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Chapter 16: Input and Output 113bit
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Chapter 16: Input and Output 115-ma
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Chapter 16: Input and Output 117The
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Chapter 16: Input and Output 119‘
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Chapter 16: Input and Output 121Thi
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Chapter 16: Input and Output 123‘
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Chapter 16: Input and Output 12516.
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Chapter 16: Input and Output 127max
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Chapter 16: Input and Output 129[nr
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Chapter 16: Input and Output 131Con
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Chapter 16: Input and Output 133SEE
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Chapter 17: Plotting 13517 Plotting
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Chapter 17: Plotting 137hold argsBu
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Chapter 17: Plotting 13917.2 Specia
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Chapter 17: Plotting 141‘#’ Set
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Chapter 17: Plotting 14317.5 Multip
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Chapter 17: Plotting 145The express
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Chapter 17: Plotting 147Note that N
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Chapter 18: Matrix Manipulation 149
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Chapter 19: Arithmetic 16319 Arithm
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Chapter 19: Arithmetic 165min (x, y
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Chapter 19: Arithmetic 16719.3 Trig
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Chapter 19: Arithmetic 16919.4 Sums
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Chapter 19: Arithmetic 171beta (a,
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Chapter 19: Arithmetic 173[x, y] =
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Chapter 20: Linear Algebra 17520 Li
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Chapter 20: Linear Algebra 177If a
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Chapter 20: Linear Algebra 179q =r
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Chapter 20: Linear Algebra 181size
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Chapter 20: Linear Algebra 183kron
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Chapter 21: Nonlinear Equations 185
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Chapter 22: Quadrature 18722 Quadra
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Chapter 23: Differential Equations
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Chapter 24: Optimization 19924 Opti
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Chapter 25: Statistics 20125 Statis
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Chapter 25: Statistics 203var (x)Fu
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Chapter 25: Statistics 205moment (x
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Chapter 25: Statistics 207[pval, ch
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Chapter 25: Statistics 209kolmogoro
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Chapter 25: Statistics 211[pval, t,
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Chapter 25: Statistics 213[pval, z]
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Chapter 25: Statistics 215binomial
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Chapter 25: Statistics 217exponenti
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Chapter 25: Statistics 219hypergeom
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Chapter 25: Statistics 221normal cd
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Chapter 25: Statistics 223t cdf (x,
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Chapter 26: Financial Functions 225
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Chapter 27: Sets 22727 SetsOctave h
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Page 333 and 334: Appendix B: Known Causes of Trouble
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Appendix C: Installing Octave 331On
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Appendix C: Installing Octave 333gc
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Appendix D: Emacs Octave Support 33
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Appendix E: Grammar 343Appendix E G
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Appendix F: GNU GENERAL PUBLIC LICE
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Concept Index 351Concept Index#‘#
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Concept Index 353Iif statement . .
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Variable Index 355Variable IndexAan
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Function Index 357Function Index(([
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Function Index 359errorbar . . . .
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Function Index 361isnumeric . . . .
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Function Index 363qzval . . . . . .
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Function Index 365vertcat. . . . .
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Operator Index 367Operator Index!!.
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