Real states of stable sliding mode control systems

摘要

States of nonlinear sliding mode control systems are considered, which approximately verify the sliding condition on the unbounded time horizon. If the equivalent control achieves uniform exponential stability, it is shown that such (real) states are ultimately bounded with arbitrarily small bound, provided the sliding error is sufficiently small. The proof requires a new converse Lyapunov theorem for constrained motions. (C) 2008 Elsevier B.V. All rights reserved.