Stability of Positive Systems in WSN Gateway for IoT&IIoT

Modern sensor networks work on the basis of intelligent sensors and actuators, their connection is carried out using conventional or specifically dedicated networks. The efficiency and smooth transmission of such a network is of great importance for the accuracy of measurements, sensor energy savings, or transmission speed. Ethernet in many networks is typically based on the TCP/IP protocol suite. Regardless of whether or not the network transmission is wired or wireless, it should always be reliable. TCP ensures transmission reliability through retransmissions, congestion control and flow control. But TPC is different in networks based on the UDP protocol. The most important here is the transmission speed achieved by shortening the header or the lack of an acknowledgment mechanism. Assuming the network is an automatic control system, it has interconnected elements that interact with each other to perform some specific tasks such as speed control, reliability and security of transmission, just the attributes that define stability being one of the fundamental features of control systems. Such a system returns to equilibrium after being unbalanced. There are many definitions of stability, e.g. Laplace or Lupanov. To check the stability of the sensor network connected to the Internet, different stability criteria should be used. We are going to analyze the stability of a computer network as a dynamic linear system, described by the equations known in the literature. In this paper, we propose the method of testing stability for positive systems using the Metzlner matrix in sensor networks such as IoT or IIoT. We will carry out tests in a place where wide area networks connect to sensor networks, that is in gates.