Robust stability of large-scale systems which contain time-invariant lur'e-type uncertainties in subsystems and norm-bounded uncertainties in interconnections

In this paper a new frequency-domain condition for the robust stability of a class of large-scale systems is derived. It is assumed that each subsystem contains one time-invariant nonlinearity satisfying a sector condition, and that the interconnecting functions are linearly bounded by the norms of the scalar outputs of subsystems. In deriving the above such Lur'e-type Lyapunov functions of subsystems are constructed so that their weighted sum is a Lyapunov function of the overall system. This condition is potential to give a sharper result than the circle-condition-type result which was obtained previously. Furthermore, a method to estimate the domain of attraction using the above Lyapunov function is also given when the sector condition is satisfied only locally.