Mu Analysis and Synthesis Toolbox

Functions - By Category

This chapter contains a detailed description of all µ-Analysis and Synthesis Toolbox (µ-Tools) functions. It begins with a list of functions in alphabetical order, followed by a list of functions grouped by subject area, and continues with a detailed description of each command. Information on each function is also available through the MATLAB on-line help facility.

In the summary of commands index and tables, the following abbreviations are used:

CONSTANT matrices are denoted by C
SYSTEM matrices are denoted by S
VARYING matrices are denoted by V

Therefore, if a command can be used with either a CONSTANT, SYSTEM or VARYING matrix, it may be denoted by CSV.

Standard Operations/Basic Functions

`abv`	Stack CSV matrices above one another
`cjt`	Conjugate transpose of SV matrices
`daug`	Diagonal augmentation of CSV matrices
`madd`	Addition of CSV matrices
`minv`	Inverse of CSV matrices
`mmult`	Multiplication of CSV matrices
`mscl`	Scale (by a scalar) a SV matrix
`msub`	Subtraction of CSV matrices
`sbs`	Stack CSV matrices next to one another
`sclin`	Scale S matrix input
`sclout`	Scale S matrix output
`sel`	Select CSV matrix rows/columns or outputs/inputs
`starp`	Redheffer star product
`transp`	Transpose of SV matrices

Matrix Information, Display and Plotting

`drawmag`	Interactive mouse-based sketch and fitting tool
`minfo`	Information on a matrix
`mprintf`	Formatted printing of a matrix
`rifd`	Display real, imaginary, frequency, and damping data
`see`	Display SV matrices
`seeiv`	Display independent variables of a V matrix
`seesys`	Formatted SV display
`unum`	Input or column dimension of a CSV matrix
`vplot`	Plotting CV matrices
`vzoom`	Mouse-driven axis selection of plot window
`wsgui`	A MATLAB workspace GUI
`xnum`	State dimension of a S matrix
`ynum`	Output or row dimension of a CSV matrix

Modeling Functions

`mfilter`	Construct a Bessel, Butterworth, Chebychev, or RC filter
`nd2sys`	Convert a SISO transfer function into a µ-Tools S matrix
`pck`	Create a S matrix from state-space data (`A, B, C, D`)
`pss2sys`	Convert an `[A B;C D]` matrix into a µ-Tools S matrix
`sys2pss`	Extract state-space matrix [A B; C D] from a S matrix
`sysic`	System interconnection program
`unpck`	Extract state-space data (`A,B,C,D`) from a S matrix
`zp2sys`	Convert transfer function poles and zeros to a S matrix

SYSTEM Matrix Functions

`reordsys`	Reorder states in a S matrix
`samhld`	Sample-hold approximation of a continuous S matrix
`spoles`	Poles of a S matrix
`statecc`	Apply a coordinate transformation to S matrices
`strans`	Bidiagonal coordinate transformation of S matrices
`sysrand`	Generate a random S matrix
`szeros`	Transmission zeros of a S matrix
`tustin`	Prewarped continuous to discrete S transformation

Model Reduction Functions

`cf2sys`	Create a S from a normalized coprime factorization
`hankmr`	Optimal Hankel norm approximation of a S matrix
`sdecomp`	Decompose a S matrix into two S matrices
`sfrwtbal`	Frequency weighted balanced realization of a S matrix
`sfrwtbld`	Stable frequency weighted realization of a S matrix
`sncfbal`	Balanced realization of coprime factors of a S matrix
`srelbal`	Stochastic balanced realization of a S matrix
`sresid`	Residualize states of a S matrix
`strunc`	Truncate states of a S matrix
`sysbal`	Balanced realization of a S matrix

SYSTEM Response Functions

`cos_tr`	Generate a cosine signal as a V matrix
`dtrsp`	Discrete-time response of a linear S matrix
`frsp`	Frequency response of a S matrix
`sdtrsp`	Sample data time response of a linear S matrix
`siggen`	Generate a signal as a V matrix
`simgui`	A GUI for time simulations of LFTs
`sin_tr`	Generate a sine signal as a V matrix
`step_tr`	Generate a step signal as a V matrix
`trsp`	Time response of a linear S matrix

H2 and H Analysis and Synthesis Functions

`dhfnorm`	Calculate discrete-time -norm of a stable S matrix
`dhfsyn`	Discrete-time H control design
`emargin`	Normalized coprime factor robust stability margin
`gap`	Calculate the gap metric between S matrices
`h2norm`	Calculate 2-norm of a stable, strictly proper S matrix
`h2syn`	H₂ control design
`hinffi`	H full information control design
`hinfnorm`	Calculate -norm of a stable, proper S matrix
`hinfsyn`	H control design
`hinfsyne`	H minimum entropy control design
`ncfsyn`	H loopshaping control design
`nugap`	Calculate the (nu) gap between S matrices
`pkvnorm`	Peak norm of a V matrix
`sdhfnorm`	Sample-data -norm of a stable S matrix
`sdhfsyn`	Sample-data H control design

Structured Singular Value (µ) Analysis and Synthesis

`blknorm`	Block norm of CV matrices
`cmmusyn`	Constant matrix µ synthesis
`dkit`	Automated D - K iteration for µ synthesis
`dkitgui`	Automated D - K iteration GUI for µ synthesis
`dypert`	Create a rational perturbation from frequency `mu` data
`fitmag`	Fit magnitude data with real, rational, transfer function
`fitmaglp`	Fit magnitude data with real, rational, transfer function
`fitsys`	Fit frequency response data with transfer function
`genphase`	Generate a minimum phase frequency response to magnitude data
`genmu`	Real and complex generalized µ-analysis of CV matrices
`magfit`	Fit magnitude data with real, rational, transfer function (a batch process)
`mu`	Real and complex µ-analysis of CV matrices
`msf`	Interactive D-scaling rational fit routine
`muftbtch`	Batch D-scaling rational fit routine
`musynfit`	Interactive D-scaling rational fit routine
`musynflp`	Interactive D-scaling rational fit routine (linear program)
`muunwrap`	Construct D-scaling and perturbation from `mu`
`randel`	Generate a random perturbation
`sisorat`	Fit a frequency point with first order, all-pass, stable transfer function
`unwrapd`	Construct D-scaling from `mu`
`unwrapp`	Construct perturbation from `mu`
`wcperf`	Worst-case performance for a given

VARYING Matrix Manipulation

`getiv`	Get the independent variable of a V matrix
`indvcmp`	Compare the independent variable data of two V matrices
`scliv`	Scale the independent variable of a V matrix
`sortiv`	Sort the independent variable of a V matrix
`tackon`	String together V matrices
`var2con`	Convert a V matrix to a C matrix
`varyrand`	Generate a random V matrix
`vfind`	Find individual elements of a V matrix
`vpck`	Pack a V matrix
`vunpck`	Unpack a V matrix
`xtract`	Extract portions of a V matrix
`xtracti`	Extract portions of a V matrix using independent variable

Standard MATLAB Commands for VARYING Matrices

`vabs`	Absolute value of a CV matrix
`vceil`	Round elements of CV matrices towards
`vdet`	Determinant of CV matrices
`vdiag`	Diagonal of CV matrices
`veig`	Eigenvalue decomposition of CV matrices
`vexpm`	Exponential of CV matrices
`vfft`	FFT for V matrices
`vfloor`	Round elements of CV matrices towards -
`vifft`	Inverse FFT for V matrices
`vimag`	Imaginary part of a CV matrix
`vinv`	Inverse of a CV matrix
`vnorm`	Norm of CV matrices
`vpinv`	Pseudoinverse of a CV matrix
`vpoly`	Characteristic polynomial of CV matrices
`vrcond`	Condition number of a CV matrix
`vreal`	Real part of a CV matrix
`vroots`	Polynomial roots of CV matrices
`vschur`	Schur form of a CV matrix
`vspect`	Signal processing `spectrum` command for V matrices
`vsvd`	Singular value decomposition of a CV matrix

Additional VARYING Matrix Functions

`vcjt`	Conjugate transpose of CV matrices
`vdcmate`	Decimate V matrices
`vebe`	Element-by-element operations on V matrices
`veval`	Evaluate general functions of V matrices
`vinterp`	Interpolate V matrices
`vldiv`	Left division of CV matrices
`vrdiv`	Right division of CV matrices
`vrho`	Spectral radius of a CV matrix
`vtp`	Transpose of CV matrices

Utilities and Miscellaneous Functions

`crand`	Complex random matrix generator (uniform distribution)
`crandn`	Complex random matrix generator (normal distribution)
`csord`	Order complex Schur form matrices
`massign`	Assign a portion of a matrix to another
`negangle`	Calculate angle of matrix elements between 0 and -2
`ric_eig`	Solve a Riccati equation via eigenvalue decomposition
`ric_schr`	Solve a Riccati equation via real Schur decomposition

Mu Analysis and Synthesis Toolbox Reference abv, daug, sbs