Central suboptimal H-∞ filter design for nonlinear polynomial systems

Abstract

<jats:title>Abstract</jats:title><jats:p>This paper presents the central finite‐dimensional <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> filter for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> filtering problem to the corresponding optimal <jats:italic>H</jats:italic><jats:sub>2</jats:sub> filtering problem, using the technique proposed in (<jats:italic>IEEE Trans. Automat. Control</jats:italic> 1989; <jats:bold>34</jats:bold>:831–847). The paper presents the central suboptimal <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> filter for the general case of nonlinear polynomial systems based on the optimal <jats:italic>H</jats:italic><jats:sub>2</jats:sub> filter given in (<jats:italic>Int. J. Robust Nonlinear Control</jats:italic> 2006; <jats:bold>16</jats:bold>:287–298). The central suboptimal <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> filter is also derived in a closed finite‐dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> filter available for the corresponding linearized system. Copyright © 2008 John Wiley &amp; Sons, Ltd.</jats:p>