Instability of closed invariant sets of semidynamical systems: method of sign-constant Lyapunov functions

DOI10.1134/S0001434609030080zbMath1185.34070MaRDI QIDQ1033937

B. S. Kalitin

Publication date: 10 November 2009

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

instabilityglobal asymptotic stabilitysemidynamical systemattracting setpositively invariant setreduction principlesign-constant Lyapunov function

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Stability theory of functional-differential equations (34K20) Stability of solutions to ordinary differential equations (34D20) Stability of manifolds of solutions to ordinary differential equations (34D35)

Related Items (5)

On criteria for asymptotic stability ⋮ On a problem of V. V. Nemytskii ⋮ Lyapunov direct method for semidynamical systems ⋮ On solving the problems of stability by Lyapunov's direct method ⋮ Properties of neighborhoods of attractors of dynamical systems

Cites Work

• Semidynamical systems in infinite dimensional spaces
• Theory of functional differential equations. 2nd ed
• Stability theory by Liapunov's direct method
• On the theorem for nonasymptotic stability in the direct Lyapunov method.
• On the reduction to a subspace of stability properties of systems in metric spaces
• On the instability of the motion of systems with retardation
• Integral manifolds and a reduction principle in stability theory
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