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.