Robust finite-time and asymptotic stability of Markovian jump Boolean networks under functional perturbations.

Abstract

This paper studies robust finite-time stability (FTS) and asymptotic stability (AS) of Markovian jump Boolean networks (MJBNs) subject to mode-dependent functional perturbations with state-independent perturbation probabilities. A semi-tensor product (STP) representation is employed to formulate the augmented Markov dynamics under perturbations. For an admissible structurally monotone perturbation class that preserves the target-to-transient block and has an elementwise nonnegative transient-to-transient error block, we establish a monotonicity property of the target-set reachability probability with respect to the perturbation vector. Together with the boundary target-invariance condition, this property yields a sufficient upper-boundary-vector check over a continuous hyperrectangular perturbation set. A two-stage bisection procedure is then developed to compute feasible mode-dependent perturbation margins for FTS and AS by updating one coordinate at a time. A 10-node neural-like Boolean network (BN) is used to illustrate the proposed method.