# YALTA: Yet Another LTI TDS Algorithm

### Overview

YALTA is a MATLAB toolbox dedicated to the stability analysis of (possibly fractionnal) delay systems with commensurate delays
given by their transfer function.
The questions YALTA can answer are :

- In the case of neutral systems
- Find the position of asymptotic axes.
- If the imaginary axis is asymptotic axis, find if the asymptotic poles of the chain are left or right the imaginary axis.

- In the case of retarded systems or of neutral systems with asymptotic axes in {Re(s) < 0}, find:
- For a given delay, the number and the position of unstable poles.
- For which values of the delay the system is stable.
- For a set of values of the delay, the position of unstable poles (root locus).
- Find (for non fractional systems) the coprime factors (N, D) of the transfer function as well as an approximation (N
_{n}, D_{n}) in H_{∞}-norm

### Contributors

David Avanessoff

Catherine Bonnet

Hugo Cavalera

André Ricardo Fioravanti

Le Ha Vy Nguyen
### Related publications

- D. Avanessoff, A.R. Fioravanti, and C. Bonnet. YALTA: a Matlab toolbox for the H
_{∞}-stability analysis of classical and fractional systems with commensurate delays. In *IFAC Joint Conference, 11th Workshop on Time-Delay Systems*, February 2013.
- R. Bellman and K. L. Cooke.
*Dierential-Dierence Equations*. Academic Press, New York, London, 1963.
- C. Bonnet, A. R. Fioravanti, and J.R. Partington. Stability of neutral systems with commensurate delays and poles asymptotic to the imaginary axis.
*SIAM Journal on Control and Optimization*, 49:498-516, 2011.
- A.R. Fioravanti, C. Bonnet, and H. Ozbay. Stability of fractional neutral systems with multiple delays and poles asymptotic to the imaginary axis. In
*IEEE Conference on Decision and Control*, Atlanta, USA, December 2010.
- A.R. Fioravanti, C. Bonnet, H. Ozbay, and S.-I. Niculescu. Stability windows and unstable poles for linear time-delay systems. In
*9th IFAC Workshop on Time-Delay Systems*, Prague, June 2010.
- A.R. Fioravanti, C. Bonnet, Hitay Ozbay, and S.-I Niculescu. A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems.
*Automatica*, 48(11):2824-2830, November 2012.
- P.M. Makila and J.R. Partington. Laguerre and Kautz shift approximations of delay systems.
*Internat. J. Control*, 72(10):932-946, 1999.
- J.R. Partington. Approximation of unstable infinite-dimensional systems using coprime factors.
*Systems and Control Letters*, 16:89-96, 1991.

### Download

Version 1.0.1 (September 28th 2015)
- Documentation
- MATLAB protected function files
- README

### Questions and discussion

If you have questions, bug reports or suggestions, please go to YALTA's forum.