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It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of dx/dt...
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
In this paper, we introduce a new class of Lyapunov functionals for analyzing hybrid dynamical systems. This class can be thought of as a generalization of the Lyapunov functional introduced by Yakubo...
The evaluation of a control-Lyapunov policy, with quadratic Lyapunov function, requires the solution of a quadratic program (QP) at each time step. For small problems this QP can be solved explicitly;...
We describe a method for truncating the coefficients of a linear controller while guaranteeing that a given set of relaxed performance constraints is met. Our method sequentially and greedily truncate...
We present an algorithmic methodology for constructing Lyapunov-Krasovskii (L-K) functionals for linear time-delay systems, using the sum of squares decomposition of multivariate polynomials to solve ...
The search for a polynomial Lyapunov function proving delay-independent stability of multivariate nonlinear polynomial delay differential equations is approached using semidefinite programming. The fu...
Problem – Extension of Principal Eigenvalue/Principal Eigenfunction Theory for Time Independent Parabolic Equations to Random Parabolic Equations I Principal Eigenvalue/Principal Eigenfunction Theo...
Metric Dynamical System Let be a probability space. Let be a metric dynamical system: (i) (ii) (iii) preserves th...
为了克服基于障碍Lyapunov 函数反演控制方法在输出约束控制中约束变量收敛区间小和要求模型精确已知的缺陷, 提出一种输出有界且全局收敛的鲁棒控制策略. 将收敛区间扩展到全局, 并使输出保持在约束区间内; 同时消除了由未知干扰和模型不确定性引起的稳态误差, 放宽了对指令信号连续可导的限制. 应用于电动舵机位置伺服控制的仿真结果表明, 舵面能够全局稳定且摆幅有界, 稳态无静差, 动态响应快, 抗扰...
将一种新型振动机构抽象为双摆的数学力学模型,分别运用矩阵QR 分解法、小球演化法以及奇异值分解法,结合计算机代数系统Mathematica,计算了模型的Lyapunov 指数.结果表明:3 种方法的计算结果基本一致,从而说明了物理双摆的混沌特征,并为双摆在工程设计中的应用提供了有价值的参考.
It has been shown that the Kullback-Leibler divergence is a Lyapunov function for the replicator equations at evolutionary stable states, or ESS. In this paper we extend the result to a more general c...
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynamical system involvin...
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.

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