Leader-following consensus considering effects of agents on each other via impulsive control: A topology dependent average dwell time approach

Leader‐following consensus and qualitative analysis of a new multi‐agent‐based epidemic model

“…Assumption 2. [27]. The communication interactions among all followers for each possible interaction graph contain a directed spanning tree, a directed tree formed by graph links that connect all the nodes and are rooted at the leader node, that is, the interaction topologies are consensusable.…”

“…Lemma 3. [27]. Consider x 1 , x 2 , and x 3 to be constant matrices satisfying x 1 = x T 1 and x 3 = x T 3 , then one may derive the following inequality…”

“…Additionally, the dynamics of people in each state can be affected by traveling between cities, which can be incorporated into the model through a new term called the ET. The concept of ET in epidemiological disease modelling was first introduced in [27] and provides a tangible representation of the effect of agents on each other in MASs.…”

“…In addition, if $$i = j,$$ then $${c}_{ij} = 0$$. Remark [27]. The modelling of the effect terms is divided into two types.…”

“…Furthermore, the authors of [27] propose a new term in MASs called "Effect Term" (ET), representing the effects of the states of agents on each other. To clarify this term in the field of epidemic disease modelling, consider the basic type of epidemic modelling called SIS, which only includes susceptible and infected people.…”