Example 8. ˙ V (x, y) = y sinx + y(−sinx)=0, and hence my V is an example of a Lyapunov function, but not strict Lyapunov function. Therefore, I can conclude, ...

How to find a strong Lyapunov's function? Example 4. It is theoretically possible to find a strong Lyapunov function for the same system as in the Example 3.

Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Definition · Basic Lyapunov theorems for... · Example

A Lyapunov function is a scalar function established on phase space that can be used to show an equilibrium point's stability.

22 мая 2024 г. · A Lyapunov function is a scalar function that can be applied to phase space to demonstrate the stability of an equilibrium point.

3 Examples. We provide you by some two dimensional examples of how to use Lyapunov functions to estimate basins of attraction. From the theorems we have to ...

30 мая 2019 г. · Lyapunov functions are nonnegative functions that decrease in time along the orbits of a dynamical system. The function L is a weak Lyapunov ...

Lyapunov Function Definition. A function that allows one to deduce stability ... Lyapunov Theorem. Lyapunov functions are useful in designing robust and adaptive.

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Опубликовано: 18 февр. 2021 г.

Proof: 1) The substitution t = t0 into (2) gives x(t0) = x0; 2) The differentiation of (2) yields (1). If f : Rn+1 7! Rn is a continuous function then the ...