双线性系统的Hamilton扩张系统

The Hamiltonian extension of bilinear systems

研究了双线性系统和它的Hamilton扩张系统的弱能控性之间的关系以及它们的能观性之间的关系,证明了双线性系统的Hamilton扩张系统是弱能控的当且仅当原双线性系统既是弱能控的又是能观的.同时给出了双线性系统的Hamilton扩张系统不能观的条件.

The relation between the weak controllability of bilinear systems and weak controllability of Hamiltonian extension system is studied. At the same time, the relation between the observability of bilinear systems and observability of Hamiltonian extension system is studied. It is proved that the Hamiltonian extension of bilinear system is controllable if and only if the bilinear system is controllable and observable. The condition that Hamiltonian extension system is not observable is given.