Ellipsoidal set-membership estimation of systems with logarithmic quantized control input

For networked control systems with logarithmic quantization, the state estimation is important. Different from the traditional state estimation methods where the uncertainties are assumed to have known probability distributions, the set-membership estimation method used in this paper only supposes that the uncertainties are bounded. This assumption is more accurate and less conservative in practical application. This paper considers the ellipsoidal set-membership estimation of discrete-time linear systems with logarithmic quantized input. The set-membership estimator, which belongs to the ellipsoid, is proposed. The estimation error is analysed, and the sufficient conditions to guarantee the boundedness of the estimation error are given. Using the sector bound property of the logarithmic quantizer, the asymptotic stability of the system and the set-membership performance constraint are analysed, respectively. According to a numerical example, it is shown that the theoretical results obtained in this paper are effective and the set-membership estimation can estimate the system state effectively. The research presents an ellipsoidal set-membership estimation for networked control systems subject to logarithmic quantized control input. It has high computational efficiency and thus has great significance.