In this work, we address the feedback stabilization problem for discrete-time reversible switched linear control systems. We focus on the question “how many state feedback gain matrices are needed for an $n$th order system with $m$ subsystems?” We prove that $n+m$ is an upper bound for the question. For completely controllable systems, a constructive design scheme is developed to steer any initial state to the origin within $\frac{n(n+1)}{2}$ steps. When the controllability is incomplete, we prove that the system is stabilizable iff the uncontrollable sub-mode is stabilizable, and propose a mixed time-driven and state-driven switching law to stabilize both the controllable sub-mode and the uncontrollable sub-mode simultaneously.

在这项工作中，我们解决了离散时间可逆开关线性控制系统的反馈稳定问题。我们关注的问题是“一个天线需要多少个状态反馈增益矩阵$ñ$具有的第阶系统 $米$子系统？” 我们证明$ñ+米$是该问题的上限。对于完全可控的系统，开发了一种建设性的设计方案以将任何初始状态引向原点。$\frac{ñ（ñ+\mathrm{1个}）}{\mathrm{2个}}$脚步。当可控性不完全时，我们证明了系统是可稳定的，前提是不可控子模式是可稳定的，并提出了混合时间驱动和状态驱动的切换定律，以同时稳定可控子模式和不可控子模式。 。