Stabilization of nonlinearly coupled uncertain systems

Concerns uncertain systems with global asymptotic stability of the zero state. It is assumed that the structure of the uncertain systems can be modelled as two nonlinearly coupled subsystems, together with uncertainty in each of the subsystems. For each uncertain system, a class of discontinuous feedback controls is presented which renders the system zero state globally asymptotically stable. The feedback stabilization problem consists of two stages. In the first, a nonlinear manifold W, containing the state origin, is constructed with the property that, if it is rendered invariant by suitable feedback, then all solutions in W tend to the state origin. In the second, a feedback control is designed which renders W both invariant and globally finite-time attractive, and the zero state of the differential inclusion system globally attractive. This manifold may be interpreted as a global centre manifold