# 耗散系统 Dissipative system

（重定向自耗散结构论

## 控制论中的耗散系统

Willems首先在系统理论中引入耗散性的概念，[7]用输入输出特性来描述动力系统。考虑一个由其状态$\displaystyle{ x(t) }$、输入$\displaystyle{ u(t) }$和输出$\displaystyle{ y(t) }$所描述的动力系统，输入-输出的相关性被给出了供给率$\displaystyle{ w(u(t),y(t)) }$。如果存在一个连续可微的存储函数$\displaystyle{ V(x(t)) }$，使得 $\displaystyle{ V(0)=0 }$, $\displaystyle{ V(x(t))\ge 0 }$$\displaystyle{ \dot{V}(x(t)) \le w(u(t),y(t)) }$.，则系统对于供给率来说是耗散的。[8]

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## 其他资料

• B. Brogliato, R. Lozano, B. Maschke, O. Egeland, Dissipative Systems Analysis and Control. Theory and Applications. Springer Verlag, London, 2nd Ed., 2007.
• Philipson, Schuster, Modeling by Nonlinear Differential Equations: Dissipative and Conservative Processes, World Scientific Publishing Company 2009.
• J.C. Willems. Dissipative dynamical systems, part I: General theory; part II: Linear systems with quadratic supply rates. Archive for Rationale mechanics Analysis, vol.45, pp. 321–393, 1972.