This paper presents a new supervisory control scheme, which is based on a control -relevant switching logic. Unlike most of the existing switching methods considering only estimator performance, the proposed scheme takes both estimator and controller performance into account. As an index to the controller performance, an iISS (integral-input-to-state stability) Lyapunov function is employed; it is ensured that the Lyapunov function satisfies a certain inequality. This Lyapunov-based switching is then coupled to the state-dependent dwell-time switching developed recently, and the state of the uncertain plant is shown to converge asymptotically. The proposed supervisory control scheme is applied to an input-constrained neurally stable linear plant. (c) 2007 Elsevier Ltd. All rights reserved.