Ads
related to: algebraic lyapunov equation example worksheet 2 pdf
Search results
Results from the WOW.Com Content Network
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. [ 1 ] [ 2 ] In particular, the discrete-time Lyapunov equation (also known as Stein equation ) for X {\displaystyle X} is
This example shows a system where a Lyapunov function can be used to prove Lyapunov stability but cannot show asymptotic stability. Consider the following equation, based on the Van der Pol oscillator equation with the friction term changed:
A Lyapunov function for an autonomous dynamical system {: Ë™ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative Ë™ = is non positive (these conditions are required on some region containing the origin).
The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number >, two n-vectors B, C and an n x n Hurwitz matrix A, if the pair (,) is completely controllable, then a symmetric matrix P and a vector Q satisfying
The Lyapunov–Malkin theorem (named for Aleksandr Lyapunov and Ioel Malkin ) is a mathematical theorem detailing stability of nonlinear systems. [ 1 ] [ 2 ] Theorem
Minimizing the drift of a quadratic Lyapunov function leads to the backpressure routing algorithm for network stability, also called the max-weight algorithm. [1] [2] Adding a weighted penalty term to the Lyapunov drift and minimizing the sum leads to the drift-plus-penalty algorithm for joint network stability and penalty minimization.
Ads
related to: algebraic lyapunov equation example worksheet 2 pdf