Ellipsoidal Toolbox

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-46.pdf

Ellipsoidal Toolbox (ET) implements in MATLAB the ellipsoidal calculus and its application to the reachability analysis of continuous- and discrete-time, possibly time-varying linear systems, and linear systems with disturbances, for which ET calculates both open-loop and close-loop reach sets. The ellipsoidal calculus provides the following benefits:

• The complexity of the ellipsoidal representation is quadratic in the dimension of the state space, and linear in the number of time steps.
• It is possible to exactly represent the reach set of linear system through both external and internal ellipsoids.
• It is possible to single out individual external and internal approximating ellipsoids that are optimal to some given criterion (e.g. trace, volume, diameter), or combination of such criteria.
• It gives simple analytical expressions for the control that steers the state to a desired target.

BibTeX citation:

```@techreport{Kurzhanskiy:EECS-2006-46,
Author = {Kurzhanskiy, Alex A. and Varaiya, Pravin},
Title = {Ellipsoidal Toolbox},
Institution = {EECS Department, University of California, Berkeley},
Year = {2006},
Month = {May},
URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-46.html},
Number = {UCB/EECS-2006-46},
Abstract = {Ellipsoidal Toolbox (ET) implements in MATLAB the ellipsoidal calculus and its application
to the reachability analysis of continuous- and discrete-time, possibly time-varying linear
systems, and linear systems with disturbances, for which ET calculates both open-loop and
close-loop reach sets. The ellipsoidal calculus provides the following benefits:
<UL>
<LI>The complexity of the ellipsoidal representation is quadratic in the dimension of the state
space, and linear in the number of time steps.
<LI>It is possible to exactly represent the reach set of linear system through both external and
internal ellipsoids.
<LI>It is possible to single out individual external and internal approximating ellipsoids that are
optimal to some given criterion (e.g. trace, volume, diameter), or combination of such criteria.
<LI>It gives simple analytical expressions for the control that steers the state to a desired target.
</UL>}
}
```

EndNote citation:

```%0 Report
%A Kurzhanskiy, Alex A.
%A Varaiya, Pravin
%T Ellipsoidal Toolbox
%I EECS Department, University of California, Berkeley
%D 2006
%8 May 6
%@ UCB/EECS-2006-46
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-46.html
%F Kurzhanskiy:EECS-2006-46
```