KMA/ODR3 Ordinary Differential Equations 3

Lecturer: Jan Andres
Lecture: 2 hours/week + exercise 1 hour/week
Credits: 3
Summer semester
Form of course completion: course credit

• Introduction to stability, historical remarks concerning the origin of the qualitative theory of ordinary differential equations.
• Notion of the Lyapunov stability of a solution (or equilibrium), uniform and asymptotic stability and instability.
• The First Lyapunov method: Routh-Hurwitz conditions, criteria of Lyapunov stability for linear systems.
• Method of linearization of nonlinear systems.
• The Second Lyapunov method: Construction of Lyapunov functions, Lyapunov stability and instability theorems.
• Lagrange stability and dissipativity in the sense of Levinson, the Yoshizawa theorem.
• Structural stability.