**Overview**

Version 2.5 features the following enhancements.

- Bug fixes to Version 2.0
- Improved algorithms and other internal changes
- New display formats
- Several new functions
- Miscellaneous updates and modifications
- Detailed information (PDF format, 700kB)

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.

Version 2.5 includes several additional display formats for polynomial matrices.

- pformat rootr Format a polynomial or polynomial entry as a product of real first- and second-order factors
- pformat rootc Format a polynomial or polynomial entry as a product of first-order factors
- pdisp Display a polynomial matrix without printing the name

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.

**axxab**

There are a number of improvements in axxab.

- By default, the macro axxab now returns a solution with triangular leading coefficient matrix (in the continuous-time case) or triangular constant coefficient matrix (in the discrete-time case). The option 'tri' is no longer effective but still valid for compatibility reasons.
- By default, the macro now uses the sparse linear system solver and performs no preliminary rank check.
- The new option 'chk ' turns the preliminary rank check on and activates MATLAB’s built-in standard (non-sparse) linear system solver.

**cgivens1**

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.

**isstable**

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

**prand**

The macro prand has two new options.

- The option 'mon ' generates a monic polynomial matrix.
- The option 'pos ' generates a polynomial matrix with the required number of zeros.

**reverse**

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

**root2pol**

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)

or

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.

**stabint**

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

© Copyright 1998 by PolyX, Ltd. All rights reserved. Polynomial Toolbox is a trademark of PolyX, Ltd. MATLAB and SIMULINK are registered trademarks of The MathWorks, Inc. Other product or brand names are trademarks or registered trademarks of their respective holders.