Robust filtering for a class of nonlinear systems via quadratic boundedness

This paper presents a new robust exponentially bounded filter for a class of uncertain nonlinear systems based on quadratic boundedness. The system under study is described by a state-space model with norm bounded noise, polytopic uncertainties, and nonlinear input meeting the sector-bounded constraints. A robust filter is designed such that the estimation error is exponentially bounded for all admissible uncertainties as well as nonlinear input. Furthermore, the minimum upper bound to the estimation error is obtained by solving a quasi-convex optimization problem of linear matrix inequality (LMI). The new LMI characterizations do not involve any product of the Lyapunov matrix and the system matrices. It enables one to check the existence of solutions by using parameter-dependent Lyapunov functions. A concrete application to Chua's circuit shows the applicability and validity of the proposed approach.