Distributed $H_{\infty}$ Sliding Mode Functional Filtering for a Class of Nonlinear Systems

This brief concerns the distributed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> sliding mode (SM) functional filter design for a class of nonlinear systems. Firstly, a novel distributed SM functional filter is designed by taking nonlinear function, disturbance, measurement output and control input into consideration. Secondly, the discontinuous control inputs are introduced to offset the influences of nonlinear terms. Thirdly, some sufficient conditions are given to ensure the asymptotic stability of SM dynamics with a prescribed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance, and the reachability of the sliding surface is ensured by using the proposed control law. Finally, the simulation of Rosser's system is given to show the validity of the proposed filter.