H ∞ control for nonlinear affine systems: a chain‐scattering matrix description approach

This paper combines an alternative chain‐scattering matrix description with ( J , J ′)‐lossless and a class of conjugate (− J , − J ′)‐lossless systems to design a family of nonlinear H ∞ output feedback controllers. The present systems introduce a new chain‐scattering setting, which not only offers a clearer expression for the solving process of the nonlinear H ∞ control problem but also removes the fictitious signals introduced by the traditional chain‐scattering approach. The intricate nonlinear affine control problem thus can be transformed into a simple lossless network and is easy to deal with in a network‐theory context. The relationship among these ( J , J ′) systems, L 2 ‐gain, and Hamilton–Jacobi equations is also given. Block diagrams are used to illustrate the central theme. Copyright © 2001 John Wiley & Sons, Ltd.