title: Set-membership fuzzy filtering for nonlinear discrete-time systems.
abstract: This paper is concerned with the set-membership filtering (SMF) problem for discrete-time nonlinear systems. We employ the Takagi-Sugeno (T-S) fuzzy model to approximate the nonlinear systems over the true value of state and to overcome the difficulty with the linearization over a state estimate set rather than a state estimate point in the set-membership framework. Based on the T-S fuzzy model, we develop a new nonlinear SMF estimation method by using the fuzzy modeling approach and the S-procedure technique to determine a state estimation ellipsoid that is a set of states compatible with the measurements, the unknown-but-bounded process and measurement noises, and the modeling approximation errors. A recursive algorithm is derived for computing the ellipsoid that guarantees to contain the true state. A smallest possible estimate set is recursively computed by solving the semidefinite programming problem. An illustrative example shows the effectiveness of the proposed method for a class of discrete-time nonlinear systems via fuzzy switch.
authors.affiliation: School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China. fwyang@ecust.edu.cn
authors.forename: Fuwen
authors.initials: F
authors.lastname: Yang
authors.forename: Yongmin
authors.initials: Y
authors.lastname: Li