Distributed $H_{\infty }$-Consensus Estimation for Random Parameter Systems Over Binary Sensor Networks: A Local Performance Analysis Method

Abstract

This paper deals with the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus estimation problem for a class of discrete time-varying random parameter systems over binary sensor networks, where the statistical information of the random parameter matrix is characterized by a generalized covariance matrix known a priori. As a binary sensor can only provide one bit of information according to a given threshold, an indicator variable is introduced so as to extract functional information (from the sensor output) that can be employed to estimate the system state. With the introduced indicator variable, a distributed estimator is constructed for each binary sensor with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus performance constraint on the estimation error dynamics over a finite horizon. By means of a local performance analysis method, indicator-variable-dependent conditions are established for the existence of the desired distributed estimators whose gains are calculated by solving a set of recursive linear matrix inequalities. Finally, the applicability and effectiveness of the developed distributed estimation scheme are demonstrated through a numerical example.