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.

1 Introduction

As a novel method with favourable finite word length performance under fast sampling rates, the delta operator modelling of discrete-time systems offers many advantages. It allows the continuous time insights to be applied to the discrete time case, for which it highlights the similarities. The delta operator also allows the effect of different choices for sampling period to be readily assessed, for which the sampling period is introduced as an exhibit parameter. In fact, the delta operator model converge to the expected continuous-time equivalents as the sampling period tends to zero.