Global stabilization of homogeneous nonlinear systems with bounded control

A bounded feedback control is designed for the global asymptotic stabilization of a class of Lyapunov stable affine systems. In general, in order to derive the bounded feedback control, the resulting procedure implies that gains, as state-functions, are obtained from the solution of a c-parameterized nonlinear programming problem. The proposed method is applied to an important class of homogeneous systems, including those systems that are globally asymptotically stabilizable by linear feedback and bilinear systems. For this class, the problem of inputs subject to global bounded rates is also addressed