Stability analysis of a parametric loop by the Lyapunov-Chetaev method

Authors

  • V. V. Beloglazov Voronezh State University, Russian Federation
  • Nikolay D. Biryuk Voronezh State University, Russian Federation
  • V. V. Yurgelas Voronezh State University, Russian Federation

DOI:

https://doi.org/10.3103/S0735272708030047

Abstract

Parametric loop has been considered as a linear oscillating circuit with positive parameters varied over time by periodic laws and having one and the same period. The thermal losses were accounted for separately for the capacitance and inductance. The free process in the circuit was investigated. The sufficient conditions of general stability were obtained by using the classical method and stability analysis was presented for a specific loop.

References

F. A. Mikhailov, E. D. Teryaev, V. P. Bulekov, et al., Dynamics of Continuous Linear Systems with Deterministic and Random Parameters (Nauka, Moscow, 1971) [in Russian].

N. G. Chetaev, Stability of Motion (OGIZ, Moscow–Leningrad, 1946) [in Russian].

A. A. Lebedev, “On One Method of Building Lyapunov’s Functions,” Prikladnaya Matematika i Mekhanika 21, No. 1, 121 (1957).

V. A. Il’in and E. G. Poznyak, Linear Algebra (Nauka, Moscow, 1984) [in Russian].

A. V. Solodov and F. C. Petrov, Linear Automatic Systems with Variable Parameters (Nauka, Mosow, 1971) [in Russian].

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Published

2008-03-04

Issue

Vol. 51 No. 3 (2008)

Section

Research Articles