Geodesic
Advanced algorithm for stability analysis of combined dynamical systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 7-16

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A hybrid dynamical system (HDS) is a system of ordinary and partial differential equations under some boundary conditions, constraints, and initial conditions. A “fast” algorithm for analyzing the stability of an HDS is applicable only in the case where the characteristic and perturbing quasipolynomials are analytic to the right of the imaginary axis and in its neighborhood. We propose an advanced algorithm for analyzing the stability of an HDS, which is free from this restriction, and compare its complexity with the “fast” algorithm.
Keywords: hybrid dynamical systems, stability theory, mathematical modeling. 
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     title = {Advanced algorithm for stability analysis of combined dynamical systems},
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D. K. Andreichenko; K. P. Andreichenko; D. V. Melnichuk. Advanced algorithm for stability analysis of combined dynamical systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 7-16. http://geodesic.mathdoc.fr/item/INTO_2021_199_a1/