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

... Lyapunov function that proves A is stable in particular: a linear system is stable if and only if there is a quadratic. Lyapunov function that proves it.

The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems ... Application to stability · Analytic solution · Discrete time

Lyapunov functions are used to certify stability or to establish invariance of a region. But the same conditions can be used to certify that the state of a ...

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

Hence V (x) = xT P−1x is our desired Lyapunov function for the dynamics xk+1 = ET xk. Note that P−1 exists and is postiive definite as eigenvalues of P−1 ...

3 сент. 2021 г. · In this section we will show that this result can be inferred from Lyapunov theory. Moreover, it will be shown that quadratic Lyapunov functions suffice.

If P > 0, Q > 0, then system is (globally asymptotically) stable. If P > 0, Q ≥ 0, and (Q, A) observable, then system is (globally asymptotically) stable.

Продолжительность: 1:39:54
Опубликовано: 14 февр. 2021 г.

Lyapunov functions are a very useful tool for investigating the behaviour of dynamical equations. They have been used now for over a century for differential ...