15 мая 2020 г. · How to derive the Lyapunov Equation? ... I have a linear dynamical system: dxdt=Ax with A∈Rn×n and x∈Rn×1. I consider a quadratic function V(x)=xT ... |
12 дек. 2022 г. · Assuming that ATP+PA=−Q holds, I want to prove that P=eATtPeATt+∫t0eATτQeATτ is a solution. |
16 апр. 2017 г. · The equilibrium x=0 of (4.22) is stable if there exists a real,symmetric, and positive definite n×n matrix P such that the matrix C given in (4.25) is negative ... |
1 апр. 2019 г. · The crux of the proof seems to rest on the fact that when we assume a non-zero c, ˙V has an upper bound −γ on the interval α≤‖x‖≤ϵ, which the ... |
19 мая 2015 г. · If A is stable, and (A,√Q) is observable, then S∞=∑∞i=0(AT)iQAi>0 is the unique solution to the algebraic Lyapunov equation: S=ATSA+Q.My ... |
16 янв. 2018 г. · I have recently come across Lyapunov's stability theorem, which states: Let 0 be an equilibrium of a differential autonomous system X′=f(X) where f is smooth. |
21 февр. 2018 г. · AP+PA=−I. It turns out that the solution to this problem is given by P=−12A−1, |
2 нояб. 2017 г. · I haven't been able to find a solid proof for the standard Lyapunov theorem related to the stability of discrete systems. |
10 окт. 2022 г. · For every symmetric and positive definite matrix Q, there exists a unique solution P to the Lyapunov equation PA+ATP=−Q, where P is positive ... |
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