Robust stability of slowly varying nonlinear systems having a continuum of equilibria

In this paper, we deal with robust stability problem for slowly time varying systems having a continuum of equilibria, whose examples are compartmental systems and adaptive control systems. For the robust analysis, we first assume that the perturbation is constant, and show existence of a Lyapunov function with specific properties for asymptotically stable systems under the constant perturbation. Next, we consider time-varying perturbation case, and show with the established Lyapunov function that state trajectories are bounded from an invariant set for bounded speed of the perturbation and that the asymptotic stability is preserved when the perturbation becomes constant as time flows.