Observer-based controller design for linear systems with limited communication capacity via a descriptor augmentation method

This study investigates the problem of observer-based control for linear time-invariant system with limited communication capacity. The system states are unavailable and the system outputs are subject to logarithmic quantisation, which can be regarded as outputs with disturbances. Traditional Luenberger observers and proportional and derivative observers are not effective to deal with such kind of estimation problems. A new estimation technique to cope with discontinuous quantised outputs is proposed such that the estimation of system states and quantisation error can be obtained simultaneously. In this design, the state variables of the derived error system are discontinuous at quantisation switching times, and traditional Lyapunov function cannot be used to perform the stability analysis. Hence, a new time-dependent Lyapunov functional and a generalised Newton-Leibniz formula are proposed to deal with this difficulty. A sufficient condition for the stability analysis of the error dynamics is established and an observer-based control scheme is proposed to stabilise the plant. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed technique.