Stability of nonlinear systems with worst case power gain disturbances

When applying nonlinear /spl Hscr//sub /spl infin// analysis, an important constraint on the system is that all trajectories decay to the origin in the absence of disturbances. In this paper, we introduce a performance measure which does not need this constraint. This allows us to analyse the likes of limit cycle systems. Unlike nonlinear /spl Hscr//sub /spl infin// analysis, we find that the dynamics in the presence of the worst case disturbance can result in a sizeable limit set S/sub w/. Often S/sub w/ bears little relation to the corresponding disturbance free limit set. We propose a Lyapunov like function W whose minimal set is precisely S/sub w/. The set S/sub w/ is invariant in that trajectories due to the worst case disturbances in forward and reverse time tend to S/sub w/.