Software for Robust Stability and Controllability
E.Mengi


I have worked on the computation of various robust stability and controllability measures during my Ph.D. thesis. Matlab implementations
of the algorithms are collected in the tar file
                -
rob_sc.tar
and in the zip file
                -rob_sc.zip
In Windows both of the files can be extracted by winzip. In Linux, Unix and Mac-OS the tar file can be extracted by typing
                    > tar -xvf rob_sc.tar
while the zip file can be uncompressed by typing
                    >unzip rob_sc.zip




Routines included:
The package includes the routines listed below. For details please see the comments at the beginning of each routine and Chapter 6 of the thesis.


Visualization routines:
-- plot_cdi
:
Plots the function that is minimized in the computation of the continuous distance to instability of a matrix.
-- plot_ddi
:
Plots the function that is minimized in the computation of the discrete distance to instability of a matrix.
-- plot_kreiss_constant_cont
:
Plots the ratio (epsln-pseudospectral abscissa)/epsln as a function of epsln.
-- plot_kreiss_constant_disc
:
Plots the ratio (epsln-pseudospectral radius-1)/epsln as a function of epsln.
-- plot_num_rad
:
Plots the function that is maximized in the computation of the numerical radius.
-- plot_poly_cdi
:
Plots the function that is minimized in the computation of the continuous distance to instability of a matrix polynomial.
-- plot_poly_ddi
:
Plots the function that is minimized in the computation of the discrete distance to instability of a matrix polynomial.
-- poly_ps
:
Plots the epsln-pseudospectra of a matrix polynomial.
-- rect_poly_ps
:
Plots the epsln-level set of the function that is minimized in the computation of the higher order distance to uncontrollability.


First order robust stability routines:
-- pspa :
Computes the epsln-pseudospectral abscissa of a matrix.
-- pspr
:
Computes the epsln-pseudospectral radius of a matrix.
-- cdi
:
Computes the continuous distance to instability of a matrix.
-- ddi
:
Computes the discrete distance to instability of a matrix.
-- numr
:
Computes the numerical radius of a matrix.


Higher order robust stability routines:
-- poly_pspa
:
Computes the epsln-pseudospectral abscissa of a matrix polynomial.
-- poly_pspr
:
Computes the epsln-pseudospectral radius of a matrix polynomial.
-- poly_cdi
:
Computes the continuous distance to instability of a matrix polynomial.
-- poly_ddi
:
Computes the discrete distance to instability of a matrix polynomial.


First order distance to uncontrollability routine:
--
dist_uncont_hybrid: Computes the distance to uncontrollability of a first order system.


Higher order distance to unconrollability routine:
--
poly_dist_uncont: Computes the distance to uncontrollability of a higher order system.


Copyright:
Copy
right for each routine is held by the authors mentioned at the start of the routine.