## 2016年5月30日月曜日

### 2016/05/30

Today I have read some part of Lyapunov Stability to learn Lyapunov function, that seems useful for reading http://www.sciencedirect.com/science/article/pii/S0947358011709773. Lyapunov function is a function that has the following energy-like properties: its value is 0 at the equilibrium point; its value is positive at any point except equilibrium point; and its value does not increase along all trajectories of the system. By Lyapunov theorem, if there exists a Lyapunov function, the equilibrium point is locally stable, that is a trajectory is "near" from the equilibrium point (the threshold of "near" can be defined arbitrarily) when the start point is enough near from the equilibrium point. I think the Monotonicity property in STORMED hybrid systems is closely related to Lyapunov function.