A remark on partial-state feedback stabilization of cascade systems using small gain theorem

This paper points out that input-to-state stability of zero dynamics having a continuously differentiable (instead of locally Lipschitz continuous) gain function suffices to guarantee the existence of globally stabilizing, smooth partial-state feedback control laws for cascade systems, without imposing any extra condition. This conclusion is proved via the small gain theorem and a novel variable separation technique combined with feedback domination design.