Path integrals and stability
Path integrals and stability
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路径积分和稳定性
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
J. Willems
中科院分区：
文献类型：
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作者：
J. Willems
与动力系统相关联的路径积分是系统变量的无记忆函数的积分，当沿着系统的轨迹积分时，仅取决于轨迹的值及其在积分区间端点处的导数。在这一章中，我们研究线性系统和二次微分形式的积分的路径独立性。这些概念和结果随后适用于稳定性问题。这导致了李雅普诺夫稳定性理论的自治系统描述的高阶微分方程，更一般的稳定性概念的系统与环境的相互作用。后者的稳定性问题与耗散系统理论密切相关。
A path integral associated with a dynamical system is an integral of a memoryless function of the system variables which, when integrated along trajectories of the system, depends only on the value of the trajectory and its derivatives at the endpoints of the integration interval. In this chapter we study path independence for linear systems and integrals of quadratic differential forms. These notions and the results are subsequently applied to stability questions. This leads to Lyapunov stability theory for autonomous systems described by high-order differential equations, and to more general stability concepts for systems in interaction with their environment. The latter stability issues are intimately related to the theory of dissipative systems.