Nonlinear \(H_\infty\) control of homogeneous systems via output feedback (Q2705725)

The paper establishes the existence of an \(H^\infty\), meaning robust, stabilizer via the output, for a certain class of nonlinear systems. The class consists of nonlinear systems, which are, however, linear in the control and where both the vector field and the output are homogeneous in the state. Furthermore, it is assumed that the system is homogeneously stabilizable and homogeneously detectable, namely, a homogeneous state feedback (of the same degree as the vector field) stabilizes the system, and, respectively, a linear feedback of the output also stabilizes the system. These properties enable a suitable quadratic Lyapunov function to be identified for the uncontrolled part, which in turn helps in the solution to the \(H^\infty\) problem.