NONLINEAR H-INFINITY CONTROL AND RELATED PROBLEMS OF HOMOGENEOUS SYSTEMS

In this paper, the problems of H-infinity control and related L-2 gain of nonlinear homogeneous systems are considered. First of all, L2 gai ns of homogeneous stable systems are estimated with a method in light of Hamilton-Jacobi inequalities. Secondly, by virtue of Hamilton-Jacob i-Isaacs (HJI) inequality, the nonlinear H-infinity(induced L-2 gain) problem of a class of systems with homogeneous vector fields is discus sed, and global control law is given under an assumption similar to th e one of stabilizability of linear systems. Then, following the previo us results, homogeneous systems with higher degree perturbed terms are studied. Finally, the analysis of finite test of homogeneous systems with perturbed parameter is presented.