ABSTRACT In this paper, the stabilisation problem of discrete-time bilinear systems by using constant control inputs is considered. It is shown that the spectrum of a matrix derived from the system matrices plays a key role in the stabilisation design. Sufficient conditions for the systems to be stabilizable by constant control inputs are presented in the cases when the derived matrix has no complex eigenvalue as well as in the cases when it has complex eigenvalues. Particularly, it is proved that, if the derived matrix has only nonzero real eigenvalues, then the systems can always be stabilised by constant control inputs. Finally, simulations are given to demonstrate the obtained results.

中文翻译：

---

通过恒定控制输入稳定离散时间双线性系统

摘要 在本文中，考虑了使用恒定控制输入的离散时间双线性系统的镇定问题。结果表明，从系统矩阵导出的矩阵的频谱在稳定性设计中起着关键作用。在导出矩阵没有复特征值的情况下以及在其具有复特征值的情况下，给出了系统通过恒定控制输入稳定的充分条件。特别地，证明了如果导出的矩阵只有非零实特征值，则系统总是可以通过恒定的控制输入来稳定。最后，给出了仿真来证明所获得的结果。