Stochastic differential equationLyapunov functionBilinear matrix inequalitiesWe present a bilinear matrix inequality (BMI) formulation of the conditions for a Lyapunov functions for autonomous, linear stochastic differential equations (SDEs). We review and collect useful results from the theory of stochastic...
1.1.7 Lyapunov Function 1.1.7.1 Definition of Lyapunov Function The core idea of Lyapunov second method is to set up a function similar to “energy” function, transform the problem of whether the system is stable into analyze the positive definite problem of the “energy” function and its fi...
关于Lyapunov Function的构造就讲到这里了,有个控制系统的研究方向就是constructive nonlinear control,是专门如何构造Lyapunov Function。其他的小众还有很多,比如Zubov’s Method(Methods of A. M. Lyapunov and Their Application), Method of Szegö(On a New Partial Differential Equation for the Stability ...
17.Estimation of Sample Lyapunov Exponent for Stochastic Differential Equation;随机微分方程的样本Lyapunov指数估计 18.Function Analysis of the Largest Lyapunov Exponent of Masseter Muscle咬肌电最大Lyapunov指数功能分析 相关短句/例句 continuous piecewise Lyapunov functions连续分段Lyapunov函数 1.Sufficient condition...
The discrete Lyapunov function is introduced to determine whether or not a solution of a scalar differential delay equation is a super-exponential solution (small solution). Furthermore, for a solution of periodic systems, the relations between the exponential decay rate, the limit of the Lyapunov...
With the aid of an appropriate Lyapunov-type function we obtain sufficient conditions guaranteeing that no finite escape time of solutions can occur. These results are then applied to open loop Nash strategies as well as to H∞-type and related Riccati differential equations. A complete solution ...
The technique which is used for this investigation is to study the relationship between the trajectories of a differential equation and its Lyapunov function. As an application of interest, we obtain characterizations of the level surfaces of a Lyapunov function and of the domain of asymptotic ...
Lyapunovstabilitytheoryofdifferentialequation solutiontodeterminetheresearchandanalysis. KeyWord:Lyapunov;stability;Vfunction. 目录 摘要.1 引言2 1预备知识3 1.1Lyapunov函数的定义3 1.2Lyapunov函数的定理3 1.2.1Lyapunov函数的定理的证明3 2.Lyapunov稳定性7 ...
Lyapunov function is a universal tool to search of the stability of dynamic systems including stationary, nonstationary, or periodic. This approach does not require the general solution of ordinary differential equations representing the system; however, it requires a Lyapunov function to be known in...
In mathematics, Lyapunov functions are functions which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions are important to stability theory and ...