Stability analysis of discrete-time general homogeneous systems

In this paper, stability analysis of discrete-time homogeneous nonlinear dynamics is considered. In particular, necessary and sufficient conditions for semiglobal KL-stability are established. These conditions lead to equivalence between semiglobal KL-stability and semiglobal exponential stability of general homogeneous dynamics. Furthermore, systematic stability analysis methods based on solving optimization problems are developed. These methods are tractable even for homogeneous systems in state spaces of high dimensions