In this section I introduce yet another powerful device to study autonomous systems of ODE. — the so-called Lyapunov functions. Let me first introduce a ...

Lyapunov function V can be thought of as generalized energy function for system. Basic Lyapunov theory. 12–6. Page 7. A Lyapunov boundedness theorem suppose ...

A system is stable at an equilibrium point if it responds to small changes from the equilibrium with only small changes in its subsequent states. Definition 2 ...

Lyapunov function is a positive definite function V such that. ˙V (x) 0 along trajectories of the system. Lyapunov functions allows various stability analysis ...

Note: (c) indicates that the PDF function V (x) = xTPx is a Lyapunov function for the system. Proof: We will demonstrate that (c) is a necessary and ...

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.

Lyapunov-Like Lemma---Example; see p. 211 of the Text. □ Interested in the stability of the origin of the system where u is bounded. □ Consider the Lyapunov ...

In the literature on system theory positive definite functions, when used to establish stability, are called Lyapunov functions. Intuitively, their physical ...

22 окт. 2024 г. · PDF | For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, ...

How to find a Lyapunov function? If the right hand side of the equation is a higher degree polynomial, then it is often convenient to find to find Lyapunov's ...