Proportional–Integral Observer Design for Uncertain Time-Delay Systems Subject to Deception Attacks: An Outlier-Resistant Approach

This article deals with the proportional–integral observer (PIO) design problem for a class of linear systems with distributed time delays and randomly occurring parameter uncertainties. The measurement signals, transmitted from the sensors to the observer, might suffer from the randomly occurring deception attacks. The random occurrences of parameter uncertainties and deception attacks are governed by two series of Bernoulli random variables with known probability distributions. An outlier-resistant PIO is developed by introducing an innovation saturation mechanism for the sake of alleviating the adverse effects induced by the deception attacks on the estimation performance. The purpose of the addressed problem is to design a PIO that is capable of guaranteeing the mean-square boundedness of the estimation errors while achieving the desired security level. The desired PIO gain is designed by solving a matrix inequality and the validity of the results obtained is shown by a numerical simulation example.