16 февр. 2018 г. · First an observation on the direct solution of the system. Add both equations to get ddt(x+y)=(x+y)−(x+y)2. which is a logistic equation for ...

21 авг. 2019 г. · There are no general steps for finding Lyapunov functions, but for low dimensional systems one can look at the stream plot and try to find a contour line.

1 июн. 2021 г. · For the linearized system dx/dt=Ax, there is an algorithmic way to find Lyapunov functions, namely take any positive definite matrix Q that you ...

13 мар. 2018 г. · You can obtain a Lyapunov by solving the algebraic Lyapunov equation for the linearization i.e. V=xTPx where P is a symmetric positive definite ...

26 окт. 2018 г. · We need to pick a Lyapunov function V(x) such that V(x) is positive definite. And we need ˙V(x) to be negative definite to prove asymptotic ...

1 авг. 2017 г. · A candidate Lyapunov function should always at least be semi-positive definite, so V(→x)≥0 ∀ →x∈Rn. In order to say something about the ...

11 нояб. 2019 г. · Solving the Lyapunov equation ATP+PA=−Q, where P is an unknown matrix, Q is any positive-definite matrix, one can obtain the solution P, which ...

28 авг. 2012 г. · A good bet is to try a polynomial as a Lyapunov function candidate. In fact, in practice, a common method is to search for a sum-of-squares polynomial.

14 мая 2017 г. · You can obtain appropriate Lyapunov functions by examining the physical dynamics of a system (obviously this is not a trivial problem depending on the system).

9 дек. 2020 г. · If the system is stable, then there exists a ball centered at the origin such that all trajectories starting in this ball are bounded.