Delta Modulator Based Quantised State-Feedback Control of Networked Linear Systems

This study proposes the design of quantised state-feedback controller using a Delta-Modulator ( $\Delta $ -M) for linear networked systems. This modulator can be considered as one type of sliding mode quantiser (SMQ) and offers several advantages such as lower design complexity, lower cost, and less noisy. The stability conditions of both the continuous-time and the discrete-time $\Delta $ -M based quantised control systems are derived. The bounds of the switching function, which ensure that the steady state behaviour of the system is periodic, are derived. The effectiveness of the $\Delta $ -M based quantised control system is investigated using a ZigBee protocol based experimental communication network with inherent imperfections associated with a real-time network. It is shown that the designed quantised state-feedback controller could achieve the desired performance.