Stability analysis of state‐triggered impulsive boolean networks based on a hybrid index model

Several real processes, such as gene expression, operate on very different timescales. This paper suggests a hybrid index model for discrete‐time impulsive systems exhibiting both macro‐ and micro‐timescale behaviors, and applies it to a stability study of state‐triggered impulsive Boolean networks (IBNs). The model conveniently characterizes the instantaneousness of jumping and essentially differs from the conventional switched‐system model. A necessary and sufficient condition for forward completeness (a basic problem in state‐triggered IBNs) is also obtained. The necessary and sufficient conditions for stability and set stability in the time and hybrid domains are derived by a quotient mapping method and a k‐domain method, respectively. The proposal results are demonstrated in examples.