Lyapunov Function Definition. A function that allows one to deduce stability is termed a. Lyapunov function. Page 50. 50. Lyapunov Function Properties for ...

Simple strong Lyapunov function. Example 2. Stability by Linearization. For the following system of equations find all equilibrium points and inves- tigate ...

So every trajectory x(t) converges to 0, i.e., ˙x = f(x) is G.A.S.. Basic Lyapunov theory. 12–10. Page 11. A Lyapunov exponential stability theorem.

Lyapunov Function Definition. A function that allows one to deduce stability is termed a. Lyapunov function. Page 50. 50. Lyapunov Function Properties for ...

In these notes we explain the power of Lyapunov functions in determining stability of equilibria and estimating basins of attraction.

For example, if we take. A(t) ⌘. 0 1. 0 1. , then xe = (1, 0)T is an equilibrium point. Definition.[Lyapunov Stability] The system (LH) is said to be stable ...

In this section we review the tools of Lyapunov stability theory. These tools will be used in the next section to analyze the stability properties.

Idea of the proof: Sufficiency follows from Lyapunov's theorem ... Example: Pendulum equation without friction. ˙x1 = x2. ˙x2 = − a sinx1. V (x) ...

Specifically, if I assume that V is a strict Lyapunov function for R2, and V (x) → ∞ for |x|→∞ then ˆx is globally asymptotically stable. 13.2 Examples. Example ...

In this section we present the Lyapunov stability method specialized for the linear time invariant systems studied in this book.