H∞ control of switched homogeneous nonlinear systems — Semi-tensor product of matrices method

This paper investigates the problems of L
₂
stability and H
_∞
control problem of a class switched homogeneous nonlinear system via the semi-tensor product (STP) of matrices method. First, a homogeneous Lyapunov-like function in the form of STP is constructed. Based on this, the system in question is limited on to the unit sphere to be investigated, a switching law is designed to make sure that the normal system that is globally asymptotically stable is globally L
₂
stable either. By the former Lyapunov-like function and the designed switching law, the H
_∞
control problem of the considered system is reduced into a Riccati-like one via the STP of matrices method, thus a control law similar to that of linear system is designed.