This paper deals with unknown input interval observer synthesis for discrete-time switched systems. First, a decomposition leading to obtain a subsystem not affected by the unknown input is presented. Second, an interval observer is designed based on the Input-to-State Stability (ISS). The gains are computed by solving Linear Matrix Inequalities (LMI) formulated based on multiple quadratic Lyapunov functions under average dwell time switching signals. In addition, a change of coordinates can be taken in order to ensure the positivity of the estimation errors. Finally, an explicit expression for the unknown input bounds is derived. Note that while the additive disturbances and the measurement noises are unknown but assumed to be bounded with known bounds, the unknown input signals are neither bounded nor stochastic.

本文涉及离散时间切换系统的未知输入间隔观测器综合。首先，提出了导致获得不受未知输入影响的子系统的分解。其次，基于输入到状态稳定性（ISS）设计间隔观察器。通过求解基于平均停留时间切换信号下的多个二次Lyapunov函数公式化的线性矩阵不等式（LMI），可以计算出增益。另外，可以采取坐标变化以确保估计误差的正性。最终，得出未知输入范围的显式表达式。请注意，虽然附加扰动和测量噪声是未知的，但假定以已知边界为界，但未知输入信号既不是有界的也不是随机的。