A polynomial approach for observer design in networked control systems with unknown packet dropout rate

In this work, the observer design for systems operating over communication networks with previously unknown packet dropout rate (PDR) is addressed. It is assumed that the PDR is time-varying and that it can be estimated online by means of the acknowledgement on new data arrival. The observer gains depend on the estimated PDR and they are designed minimizing the H1 norm from disturbances and measurement noises to estimation error over all the possible PDRs. The observer gains are rational (including as a particular case a polynomial) functions of the estimated PDR of the desired order. An optimization over polynomials has been carried out in order to find a solution for the proposed filter.