Lyapunov-based stability of time-triggered impulsive logical dynamic networks

In this paper, we consider the stability of impulsive logical dynamic systems (ILDNs) from two aspects: impulsive disturbance and impulsive control. The existing results on the stability of ILDNs only consider the stability of ILDNs under a given impulsive instant sequence (IIS), which has some limitations and motivates us to consider the stability of ILDNs under any IIS. By constructing a merged ILDN, under the assumption that the non-impulsive process and impulsive process are all globally stable, a necessary and sufficient condition on the stability of ILDNs under any IIS is proposed at first. Unfortunately, the obtained result is too restrictive, and in practice, it is not common that a stable LDN is still stable under any IIS. The fact is that for any stable LDN, there exist some IISs such that its stability is destroyed, and these IISs are called impulsive disturbances; for any unstable LDN, there exist some IISs such that the stability can be achieved, and these IISs are called impulsive control. To investigate the stability of ILDNs, the concept of average impulsive interval is first introduced to ILDNs, and several sufficient conditions are proposed to ensure the stability of LDNs under the time-triggered IISs with the property of average impulsive interval. Moreover, the obtained results are applied to the set stability of ILDNs.(c) 2023 Published by Elsevier Ltd.

Automated summary

This paper investigates the stability of impulsive logical dynamic systems (ILDNs) from the perspectives of impulsive disturbance and impulsive control. The existing results on ILDN stability only consider a given impulsive instant sequence (IIS), which is restrictive. The paper proposes necessary and sufficient conditions for ILDN stability under any IIS by constructing a merged ILDN. However, these conditions are too strict as it is uncommon for a stable LDN to remain stable under any IIS. The paper introduces the concepts of impulsive disturbances and impulsive control, and presents sufficient conditions for LDN stability under time-triggered IISs with average impulsive interval. These results are also applied to set stability of ILDNs.