H infinity control, stabilization, and input-output stability of nonlinearsystems with homogeneous properties

In this paper, we discuss the problems about H-infinity control, stabilizat ion and input-output stability of nonlinear systems, which may not satisfy known regularity conditions related to smoothness. To this end, a class of homogeneous systems and systems that can be approximated by homogeneous sys tems, are concentrated on. New relationships are established between H-infi nity control and stabilization, and between L-p stability and Lyapunov stab ility. At first, with Hamilton-Jacobi-Isaacs inequality, the nonlinear H-in finity control problem of the systems with homogeneous properties is discus sed. The results show that their stabilizability via homogeneous feedback, in the case without exogenous input signals, implies the solvability of the ir H-infinity control problem. Then, simply formulated results on input-out put stability are obtained, based on the relations among the homogeneity de grees concerned with the considered systems. The conclusions hold globally for homogeneous systems and locally for those that can be homogeneously app roximated. (C) 2001 Elsevier Science Ltd. All rights reserved.