Observer Design and Observer-Based Robust H ∞ Feedback Control for Positive Delta Operator Systems with Time-Delays

This paper focuses on observer and observer-based robust
$H$

∞
feedback controller design for positive delta operator systems with time-delays. First of all, a positive observer is designed to estimate the states of the proposed positive system, which is a Luenberguer-type and ensures the estimation to be nonnegative at any time. Moreover, an observer-based robust
$H$

∞
feedback control problem is considered for further study. New sufficient conditions for the existence of the desired controller are derived as LMIs such that the resulting closed-loop system is positive and asymptotically stable simultaneously. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed approach.