ON THE DESIGN OF HIGH-ORDER ROBUST LINEAR H∞ FILTERS FOR A CLASS OF UNCERTAIN NONLINEAR SYSTEMS

Abstract

This paper addresses the design of robust linear H∞ filters for a class of nonlinear systems subject to uncertain, possibly time-varying, parameters. The nonlinear system is described by a differential-algebraic representation, which can model the whole class of systems with rational functions of the state and uncertain parameters, as well as some trigonometric nonlinearities. The admissible values of the uncertain parameters and their rate of variation are assumed to belong to a given polytope. A linear matrix inequality (LMI) method is presented to design full-order robust linear filters with a minimized upper-bound on the &ℒ2-gain of the noise-to-estimation error operator for all admissible uncertainty. An LMI procedure based on the latter method is then developed to obtain high-order robust linear filters, which are shown, via an example, to achieve significant performance improvement over the full-order filter.