Nonlinear H∞ control of switched homogeneous nonlinear systems

In this paper, the problem of L
₂
stability and H
_∞
control of switched homogenous systems is addressed. Based on the homogenous properties of the systems, the considered systems are limited to a unit sphere for investigation. First of all, the problem of L
₂
stability of the switched homogeneous systems is discussed via a designed switching law under the absence of control items, it is shown that, similar to linear case, the stability of normal systems implies to L
₂
stability under a given switching law. Then H
_∞
control problem of switched homogeneous systems is investigated. Similar to Algebraic Riccati Inequality for H
_∞
control of switched linear systems, a condition for global control laws to solve H
_∞
control problem is obtained for the switched homogeneous nonlinear systems, which are preferable and easier verified compared to the existing results for switched nonlinear systems.