Simultaneous State and Unknown Input Interval Observer for Discrete-Time Linear Switched Systems Using Peak-to-Peak Analysis

This paper investigates interval observer design for uncertain discrete-time linear switched systems under unknown inputs and a known switching signal. The approach introduces weighting matrices which allow one to relax design difficulties caused by classical coordinate transformation. To improve the accuracy, an
$L_{\infty}$
method minimizing the peak-to-peak gain is employed to reduce the influence of unknown uncertainties. The interval observer gains are computed by solving Linear Matrix Inequality (LMI) formulated based on multiple quadratic Lyapunov functions under average dwell time switching signals.