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第114行： − − − :<math> \dot{V}(x(t)) \le w(u(t),y(t))</math>.<ref>{{cite book |last1=Arcak |first1=Murat |last2=Meissen |first2=Chris |last3=Packard |first3=Andrew |title=Networks of Dissipative Systems |date=2016 |publisher=Springer International Publishing |isbn=978-3-319-29928-0 }}</ref>
→控制论中的耗散系统 Dissipative systems in control theory
In systems theory the concept of dissipativity was first introduced by Willems, which describes dynamical systems by input-output properties. Considering a dynamical system described by its state <math> x(t) </math>, its input <math>u(t)</math> and its output <math>y(t)</math>, the input-output correlation is given a supply rate <math> w(u(t),y(t))</math>. A system is said to be dissipative with respect to a supply rate if there exists a continuously differentiable storage function <math> V(x(t))</math> such that <math>V(0)=0</math>, <math>V(x(t))\ge 0 </math> and
In systems theory the concept of dissipativity was first introduced by Willems, which describes dynamical systems by input-output properties. Considering a dynamical system described by its state <math> x(t) </math>, its input <math>u(t)</math> and its output <math>y(t)</math>, the input-output correlation is given a supply rate <math> w(u(t),y(t))</math>. A system is said to be dissipative with respect to a supply rate if there exists a continuously differentiable storage function <math> V(x(t))</math> such that <math>V(0)=0</math>, <math>V(x(t))\ge 0 </math> and
:<math> \dot{V}(x(t)) \le w(u(t),y(t))</math>.<ref>{{cite book |last1=Arcak |first1=Murat |last2=Meissen |first2=Chris |last3=Packard |first3=Andrew |title=Networks of Dissipative Systems |date=2016 |publisher=Springer International Publishing |isbn=978-3-319-29928-0 }}</ref>
在系统论中，耗散性的概念是由 Jan Camiel Willems 首先提出的，它通过输入输出的性质来描述动态系统。考虑一个由状态 x (t) / math 描述的动力系统，它的输入数学 u (t) / math 和输出数学 y (t) / math，输入输出相关性被给出一个供给率数学 w (u (t) ，y (t) / math。如果存在一个连续可微的存储函数数学 v (x (t)) / 这样的数学 v (0)0 / math，数学 v (x (t)) ge0 / math，那么系统相对于供给率是耗散的
在系统论中，耗散性的概念是由 Jan Camiel Willems 首先提出的，它通过输入输出的性质来描述动态系统。考虑一个由状态 x (t) / math 描述的动力系统，它的输入数学 u (t) / math 和输出数学 y (t) / math，输入输出相关性被给出一个供给率数学 w (u (t) ，y (t) / math。如果存在一个连续可微的存储函数数学 v (x (t)) / 这样的数学 v (0)0 / math，数学 v (x (t)) ge0 / math，那么系统相对于供给率是耗散的
<math> \dot{V}(x(t)) \le w(u(t),y(t))</math>.
<math> \dot{V}(x(t)) \le w(u(t),y(t))</math>.