We present a novel state feedback design method for perturbed discrete-time switched linear systems. The method aims at achieving (a) closed-loop stability under arbitrary switching and (b) minimisation of ultimate bounds for specific state components. Objective (a) is achieved by computing state feedback matrices so that the closed-loop $A$ matrices generate a solvable Lie algebra (i.e. admit simultaneous triangularisation). Previous results derived an iterative algorithm that computes the required feedback matrices, and established conditions under which this procedure is possible. Based on these conditions, objective (b) is achieved by exploiting available degrees of freedom in the iterative algorithm.
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机译：我们提出了一种用于扰动离散时间切换线性系统的新型状态反馈设计方法。该方法旨在在任意切换下实现（a）闭环稳定性，（b）最小化特定状态分量的最终范围。通过计算状态反馈矩阵实现目标（a），使得闭环$ a $矩阵产生可溶性Lie代数（即承认同时三角形）。以前的结果派生了一种迭代算法，该算法计算所需的反馈矩阵，以及该过程的建立条件。基于这些条件，目标（b）通过利用迭代算法的可用程度来实现。
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