Necessary and sufficient stability conditions for time-delay systems: a comparison

https://doi.org/10.58571/CNCA.AMCA.2022.018

Resumen: We compare three existing criteria which provide necessary and sufficient stability conditions for linear time-delay systems. An outstanding property of these conditions, based on the delay Lyapunov matrix, is that the decision is made via a finite number of operations. The main ideas of each method are briefly introduced and tested on two illustrative examples. A discussion of the result is presented.

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Alejandro Castaño, Oscar Santos-Estudillo, Gerson Portilla & Sabine Mondié. Necessary and sufficient stability conditions for time-delay systems: a comparison. Memorias del Congreso Nacional de Control Automático, pp. 50-55, 2022. https://doi.org/10.58571/CNCA.AMCA.2022.018

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Control de Sistemas Lineales; Otros Tópicos Afines

• Alexandrova, I.V. (2022). A finite lyapunov matrix-based stability criterion via piecewise linear approximation. Submitted to MTNS 2022.
• Bajodek, M., Gouaisbaut, F., and Seuret, A. (2022). Necessary and sufficient stability condition for timedelay systems arising from legendre approximation. Hal-03435028v2.
• Egorov, A.V. (2014). A new necessary and sufficient stability condition for linear time-delay systems. IFAC Proceedings Volumes, 47(3), 11018–11023.
• Egorov, A.V. (2016). A finite necessary and sufficient stability condition for linear retarded type systems. In 2016 IEEE 55th Conference on Decision and Control (CDC), 3155–3160. IEEE.
• Egorov, A.V. and Mondi´e, S. (2014). Necessary stability conditions for linear delay systems. Automatica, 50(12), 3204–3208.
• Egorov, A. and Mondie, S. (2014b). Necessary conditions for the exponential stability of time-delay systems via the lyapunov delay matrix. International Journal of Robust and Nonlinear Control, 24(12), 1760–1771.
• Gomez, M.A., Egorov, A.V., and Mondi´e, S. (2019). Lyapunov matrix based necessary and sufficient stability condition by finite number of mathematical operations for retarded type systems. Automatica, 108, 108475.
• Kharitonov, V.L. (2013). Time-delay systems: Lyapunov functionals and matrices. Basel: Birkhauser.
• Kharitonov, V.L. and Zhabko, A.P. (2003). Lyapunov–krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 39(1), 15–20.
• Krasovskii, N. (1956). On the application of the second method of lyapunov for equations with time delays. Prikl. Mat. Mekh, 20(3), 315–327.
• Medvedeva, I.V. and Zhabko, A.P. (2013). Constructive method of linear systems with delay stability analysis. IFAC Proceedings Volumes, 46(3), 1–6.
• Mondie, S., Egorov, A.V., and Gomez, M.A. (2018). Stability conditions for time delay systems in terms of the lyapunov matrix. IFAC-PapersOnLine, 51(14), 136–141.
• Neimark, J. (1949). D-subdivisions and spaces of quasipolynomials. Prikladnaya Matematika i Mekhanika, 13(5), 349–380.