Application of Quadratic Lyapunov Functions to Investigation of Stability of Systems with Delay
- 2 Downloads
When studying systems with delay, a particular attention is paid to such important property as their stability. In investigation of stability of systems of ODEs by the direct Lyapunov method, quadratic Lyapunov functions are widely used. For a system with delay, we suggest to use as Lyapunov functions some quadratic Lyapunov functions constructed for a system of ODEs and satisfying some restrictions on the first derivative. For such systems we find conditions which make possible to use such quadratic functions as Lyapunov functions.
Key wordssystem with delay stability direct Lyapunov method quadratic Lyapunov function
Unable to display preview. Download preview PDF.
- 2.Barbashin, E.A. Lyapunov Functions (Nauka, Moscow, 1970) fin Russian].Google Scholar
- 3.Kim, A.V. Direct Lyapunov’s Method for Systems with Delays (Ural University, Ekaterinburg, 1992) fin Russian].Google Scholar
- 4.Razumikhin, B.S. Stability of Ereditar Systems (Nauka, Moscow, 1988) fin Russian].Google Scholar
- 5.Krasovskii, N.N. “On asymptotical stability of systems with delay”, Prikl. Mat. Mech.20(4), 513–518 (1956) fin Russian].Google Scholar
- 6.Krasovskii, N.N. Some Problems of the Theory of Stability of Motions (Gostehizdat, Moscow, 1959) [in Russian].Google Scholar
- 8.Rasumikhin, B.S. “Application of method of Liapunov to problems of stability of delay systems”, Avtomat. i Telemekh.21(6), 740–748 (1960) fin Russian].Google Scholar