Domains of attraction of interconnected systems: A Zubov method approach

We study feedback interconnections of two nonlinear systems, that are asymptotically stable at a fixed point. It is shown that if the subsystems are input-to-state stable and the corresponding gains satisfy a small gain condition, then estimates for the domain of attraction of the whole system may be obtained by calculating robust Lyapunov functions for the subsystems. The latter task can be solved using available Zubov techniques. In total this approach makes numerical computations feasible, as high cost computations only have to be performed in lower dimensions. This comes at the price, that in general only lower approximations of the domain of attraction are obtained and that the system has to be brought into a form, where a small gain condition holds.