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