## 1 Introduction  
Complex networks can be defined as a set of elements called nodes that are interconnected with each other through links. The number of nodes is often too large, which makes the individual nature of each node and link somewhat complex. The meaning of both nodes and links can vary depending on the desired approach. Given this, the nodes of a complex network can be, for example, people, and the link between these people can be any situation where they have spoken to each other, or they can be dynamic systems with interconnections between them where the states of one system can influence those of the other system [1; 2; 3; 4]. The intrinsic phenomena of complex networks, like the loss of connections, cannot be captured using fixed connections. The significance of dynamic complex networks lies in their practical relevance, as the interactions within these systems and their interconnected nodes are typically dynamic rather than static. There are interesting studies on complex networks with time-varying connections, especially [5], in which the variations of the connections were considered bounds. Furthermore, in the study [6], a complex network with variant connections was synchronized through impulse. However, both works are focused on continuous-time complex networks. The interconnection of systems in our world occurs naturally. One example is the way that different lifeforms relate and interact with each other, matter itself is naturally interconnected, or even key aspects of modern life such as the internet are examples of these interconnections; this highlights the importance of studying complex networks, which have numerous valuable applications, including infectious disease modeling, autonomous vehicles, mobile robotics, and electric systems, among others [1; 2; 3; 4]. As previously mentioned, nodes of a complex network can be described as systems with their own dynamics, and the network as a whole can also be viewed as a dynamic system. In control theory, the goal is for dynamic systems to have a desired behavior, and this is achieved through the design of controllers. There are many different types of algorithms to achieve this goal, some are developed using traditional methods based on mathematical models, while others are designed using modern methodologies such as those based on neural networks; the use of any particular methodology is based on the control design. A commonly used control algorithm for complex networks is PIN-type control, where only a limited number of nodes of the network are locally controlled. This type of control methodology is used since the alternative of controlling every single node locally can be impossible when dealing with a great number of nodes in a network or when controlling every node is deemed unnecessary. PIN-type control has been widely studied previously and has been improved by being combined with other control methodologies such as sliding mode control, inverse optimal control or neural networks. On the other hand, impulse control is a methodology that is not specific to complex networks where control signals are not applied continuously but rather in time instants defined by the application requirements. This type of control is well suited for the control of biomedical systems since treatment medication as well as vaccination schemes are typically administered in an impulse manner at determined time intervals [1; 2; 3; 4]. Furthermore, infectious disease transmission is a complex phenomenon where numerous factors intervene such as the host and pathogen environment, exposed population, and population dynamics, among many other aspects [7]. The goal of epidemiological mathematics is to model the implantation and expansion of pathogens in each population.