The nature of solutions to linear passive complementarity systems
The nature of solutions to linear passive complementarity systems
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线性无源互补系统解决方案的本质
DOI：
10.1109/cdc.1999.831401
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
J. Schumacher
中科院分区：
文献类型：
--
作者：
M. K. Çamhbel;W. Heemels;J. Schumacher
研究了具有互补条件的线性无源系统(作为应用，可以考虑具有理想二极管的线性无源网络)。对于包含在混杂系统的线性互补类中的这些系统，建立了解的存在唯一性。此外，对解决方案的性质进行了表征。特别地，证明了狄拉克脉冲的导数不可能发生，而状态变量中的狄拉克脉冲和跳跃只能在t=0时发生。这些事实在某种意义上降低了解决方案的“复杂性”。最后，我们给出了没有狄拉克脉冲或状态变量不连续的初始状态集的显式刻画。事实证明，这组“规则状态”在动态下是不变的。
Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the nature of the solutions is characterized. In particular, it is shown that derivatives of Dirac impulses cannot occur and Dirac impulses and jumps in the state variable can only occur at t=0. These facts reduce the 'complexity' of the solution in a sense. Finally, we give an explicit characterization of the set of initial states from which no Dirac impulses or discontinuities in the state variable occur. This set of 'regular states' turns out to be invariant under the dynamics.