H ∞ control, stabilization and input output stability of nonlinear systems based on homogeneous techniques 1

Abstract

Abstract In this paper, new relationships are studied between H∞ control and stabilization of (homogeneous) nonlinear control systems, and between Lp stability and Lyapunov stability of (homogeneous) nonlinear systems. In the first part, by virtue of Hamilton-Jacobi-Isaacs (HJI) inequality, nonlinear H∞ control problems of stabilizable homogeneous systems and the systems that can be approximated by homogeneous ones are discussed for their designs. One of the main results is that, if the considered system, without exogenous input signals, can be stabilized via homogeneous feedback, then its H^a control problem can be solved with continuous (but maybe noiismooth) feedback laws. In the second part, the problem of input-output stability (IOS) is considered with relations among the lowest homogeneity degrees of the terms of considered systems, and both global and local results are obtained in different cases