Lyapunov theory
- 1. Lyapunov Theory Sistem Non Linear Aditya A. Purnama / 1410501023 Dosen Pembimbing : R. Suryoto Edy Raharjo, S.T., M.Eng
- 2. Table of content • Stability • Positive definite functions • Lyapunov stability theorems • Converse Lyapunov theorems • Finding Lyapunov functions
- 3. Stability • Stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. • In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance. • In dynamical systems, an orbit is called Lyapunov stable if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood.
- 7. Converse Lyapunov theorems • A typical converse Lyapunov theorem has the form
- 8. Finding Lyapunov functions • There are many different types of Lyapunov theorems the key in all cases is to find a Lyapunov function and verify that it has the required properties • There are several approaches to finding Lyapunov functions and verifying the properties • Decide form of Lyapunov function (e.g., quadratic), parametrized by some parameters (called a Lyapunov function candidate) • Try to find values of parameters so that the required hypotheses hold
- 9. TERIMA KASIH Daftar Pustaka : https://en.wikipedia.org/wiki/Stability_theory https://en.wikipedia.org/wiki/Lyapunov_function https://en.wikipedia.org/wiki/Lyapunov_equation http://stanford.edu/class/ee363/lectures/lyap.pdf http://stanford.edu/class/ee363/lectures/lq-lyap.pdf