Robust controllability and stabilization of switched Boolean control networks subject to multi-bit function perturbations

Abstract

This paper develops a new multi-bit perturbed controllability matrix method for solving the robust controllability and stabilization of switched Boolean control networks (SBCNs) with multi-bit function perturbations. By constructing both perturbed position index matrix and multi-bit perturbed controllability matrix for SBCNs, the space of state pairs is divided into two disjointed parts, which determine whether or not the paths between two arbitrary states are affected by function perturbations. Then, a sequence of perturbed reachable sets is constructed, and several criteria are presented for the robust controllability of SBCNs under the multi-bit function perturbations. As a generalization, a perturbed position index matrix and a sequence of perturbed reachable sets are designed for the closed-loop system, based on which, a necessary and sufficient condition is presented for the robust state-feedback stabilization of SBCNs under arbitrary switching signal. Numerical examples demonstrate that our new criteria work well for the multi-bit function perturbations and thus have more practical significance.