Upgrade Information for Version 2.5


Version 2.5 features the following enhancements.

Bug fixes

Version 2.5 includes a number of bug fixes. In particular, it includes all patches that were made available on the PolyX website since the release of Version 2.0.


Improved algorithms and other internal changes

Several algorithms have been improved in Version 2.5 to reflect recent research achievements. In particular, the linear polynomial matrix equation solvers axb, axbyc, xab, xaybc, and axxa2b perform faster, in particular for large matrices. These modifications have no impact on the way the functions are used and hence require no attention on the part of the user. In particular, no changes were made in the numbers of input and output arguments and their order.


New display formats

Version 2.5 includes several additional display formats for polynomial matrices.

New functions

Several new functions were added in Version 2.5.

LaTeX formatting of polynomial matrices
The new routine
pol2tex is a great help for authors who use LaTeX.
pol2tex     Formats a polynomial matrix for use in a LaTeX document

H2 optimization
Version 2.5 offers two new solutions for the standard H-2 problem under quite general conditions.
h2         Polynomial solution of the standard H-2 optimization problem
dssh2    Descriptor solution of the standard H-2 optimization problem

Interval polynomials
Version 2.5 adds the following new macros to the already impressive list of routines for testing the stability of interval polynomials
jury Create the Jury matrix corresponding to a polynomial
sarea, sareaplot     Robust stability area for polynomials with parametric uncertainties
spherplot     Plot the value set ellipses for a spherical polynomial family
tsyp     Use the Tsypkin-Polyak function to determine the .robustness margin for a continuous interval polynomial
vset,vsetplot     Value set of parametric polynomial. A tool for robust stability testing via Zero Exclusion Condition

State space systems
Version 2.5 includes two polynomial methods for state space systems
psseig Polynomial approach to eigenstructure assignment for state-space sys-tem
psslqr Polynomial approach to linear-quadratic regulator design for state-space system

Simulink routines
Two brand new routines allow the automatic conversion of
SIMULINK block diagrams to LMF and RMF descriptions.
sim2lmf Simulink-to-LMF description of a dynamic system
sim2rmf Simulink-to-RMF description of a dynamic system

Numerical routines
Version 2.5 includes two upgrades of existing numerical utilities and a new numerical function.

clements1 Conversion to Clements standard form (upgrade of clements)
dssreg “Regularizes” a standard descriptor plant (upgrade)
gare Solution of the generalized algebraic Riccati equation

Polynomial matrix functions
The function complete is a new addition to the collection of polynomial matrix functions.
complete Complete a non-square polynomial matrix to a square unimodular ma-trix

Demos and shows
Three new text based demos have been included in Version 2.5. They are self-explanatory and no documentation is available. Simply type the name of the demo in the command line.
poldemo This demo reviews several of the functions and operations defined in the Polynomial Toolbox for polynomials and polynomial matrices
poldemodebe Design of a dead-beat compensator
poldemodet Comparison between numerical and symbolic computation of determi-nant of a polynomial matrix. This demo requires the Symbolic Toolbox to be installed

In addition two “shows” have been prepared that run in a graphical interface. Enter the name of the show in the command line to view the show. No additional documentation is available.
poltutorshow Introduction into the basic operations with polynomials and polynomial matrices. This is a graphical version of the text based demo poldemo
polrobustshow Overview of parametric robust control tools


Miscellaneous updates and modifications

This section lists modifications in various macros that were made after Version 2.0 was released. The changes leave the macros fully compatible with Version 2.0 and are all reflected in the on-line help.

There are a number of improvements in axxab.

The macro cgivens1 differs from the implementation in Version 2.0 by the introduction of an optional tolerance tol. The default value of tol is 0. In the form

[c,s] = cgivens1(x,y,tol)

the routine sets x and y equal to zero if their magnitude is less than tol.

Unimodular polynomial matrices and constant non-polynomial matrices are now considered to be stable, and not unstable as in Version 2.0.

The macro prand has two new options.

The function call reverse(P) with the single input argument P, reverses the order of the coefficients.

Zeroing management has been changed in this macro. Now, no zeroing is performed by default. However, an optional tolerance tol may be passed to the macro in one of the forms

P = root2pol(Z,K,tol)


P = root2pol(Z,K,tol,var)

In this case all coefficients of the resulting polynomial that are less than tol times the largest coefficient are neglected. Note that if the tolerance argument is included both the input argument Z and K needs to be present.

The on-line help has been modified to emphasize that the routine does not work with complex polynomials.


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