TRACE-DDE: a Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations. In the recent years the authors developed numerical schemes to detect the stability properties of different classes of systems involving delayed terms. The base of all methods is the use of pseudospectral differentiation techniques in order to get numerical approximations of the relevant characteristic eigenvalues. This chapter is aimed to present the freely available Matlab package TRACE-DDE devoted to the computation of characteristic roots and stability charts of linear autonomous systems of delay differential equations with discrete and distributed delays and to resume the main features of the underlying pseudospectral approach.

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  1. Ramírez, Adrián; Breda, Dimitri; Sipahi, Rifat: A scalable approach to compute delay margin of a class of neutral-type time delay systems (2021)
  2. Zhang, Lu; Li, Xu-Guang; Mao, Zhi-Zhong; Chen, Jun-Xiu; Fan, Gao-Xia: Some new algebraic and geometric analysis for local stability crossing curves (2021)
  3. Nechepurenko, Yuri; Khristichenko, Michael; Grebennikov, Dmitry; Bocharov, Gennady: Bistability analysis of virus infection models with time delays (2020)
  4. Gomez, Marco A.; Michiels, Wim; Mondié, Sabine: Design of delay-based output-feedback controllers optimizing a quadratic cost function via the delay Lyapunov matrix (2019)
  5. Pradhan, Saroj P.; Hartung, Ferenc; Turi, Janos: Dynamics in a respiratory control model with two delays (2019)
  6. Ariyatanapol, Rittirong; Xiong, Y. P.; Ouyang, Huajiang: Partial pole assignment with time delays for asymmetric systems (2018)
  7. Barbarossa, M. V.; Polner, M.; Röst, G.: Stability switches induced by immune system boosting in an SIRS model with discrete and distributed delays (2017)
  8. Kiss, Gabor; Lessard, Jean-Philippe: Rapidly and slowly oscillating periodic solutions of a delayed van der Pol oscillator (2017)
  9. Ulsoy, A. Galip: Improving stability margins via time-delayed vibration control (2017)
  10. Pradhan, S. P.; Turi, J.: Effects of CPAP therapy on respiratory control system stability (2016)
  11. Sánchez Sanz, Julia; Getto, Philipp: Numerical bifurcation analysis of physiologically structured populations: consumer-resource, cannibalistic and trophic models (2016)
  12. Cepeda-Gomez, Rudy; Michiels, Wim: Some special cases in the stability analysis of multi-dimensional time-delay systems using the matrix Lambert (W) function (2015)
  13. Seuret, Alexandre; Gouaisbaut, Frédéric; Ariba, Yassine: Complete quadratic Lyapunov functionals for distributed delay systems (2015)
  14. Gumussoy, Suat; Gahinet, Pascal: Computer Aided Control System design for time delay systems using MATLAB(^\circledR) (2014)
  15. Qiao, Wei; Sipahi, Rifat: Delay-dependent coupling for a multi-agent LTI consensus system with inter-agent delays (2014)
  16. Semenič, Nikolaj; Sarjaš, Andrej; Chowdhury, Amor; Svečko, Rajko: Quasipolynomial approach to simultaneous robust control of time-delay systems (2014)
  17. Vyhlídal, Tomáš; Zítek, Pavel: QPmR-quasi-polynomial root-finder: algorithm update and examples (2014)
  18. Yi, Sun; Duan, Shiming; Nelson, Patrick W.; Ulsoy, A. Galip: Analysis and control of time delay systems using the LambertWDDE Toolbox (2014)
  19. Diekmann, O.; Korvasová, K.: A didactical note on the advantage of using two parameters in Hopf bifurcation studies (2013)
  20. Nakaoka, Shinji; Aihara, Kazuyuki: Stochastic simulation of structured skin cell population dynamics (2013)

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