In this article, an engineering/physical dynamic system including losses is analyzed inrelation to the stability from an engineer’s/physicist’s point of view. Firstly, conditions for a Hamiltonian to be an energy function, time independent or not, is explained herein. To analyze stability of engineering system, Lyapunov-like energy function, called residual energy function is used. The residual function may contain, apart from external energies, negative losses as well. This function includes the sum of potential and kinetic energies, which are special forms and ready-made (weak) Lyapunov functions, and loss of energies (positive and/or negative) of a system described in different forms using tensorial variables. As the Lypunov function, residual energy function is defined as Hamiltonian energy function plus loss of energies and then associated weak and strong stability are proved through the first time-derivative of residual energy function. It is demonstrated how the stability analysis can be performed using the residual energy functions in different formulations and in generalized motion space when available. This novel approach is applied to RLC circuit, AC equivalent circuit of Gunn diode oscillator for autonomous, and a coupled (electromechanical) example for nonautonomous case. In the nonautonomous case, the stability criteria can not be proven for one type of formulation, however, it can be proven in the other type formulation.

The paper puts forward and implements a method of designing and creating a modelling simulation environment for extensive and complete analysis of economical lighting on highways. From a general design viewpoint, the proposed solution explores the concept of a network description language (SMOL), which has been designed to describe the necessary network functions, mechanisms, and devices for the purpose of their computer simulation and verification. The presented results of the performed research confirm the usability of intelligent lighting on highways, both in the sense of the design concept and in the aspect of saving energy.

Modeling and simulation are key performance analysis and control techniques to optimize decision-making as well as design and operate complex production systems. They are also indicated as one of the technological pillars of modern industry and IT solutions supporting the implementation of the roadmap toward Industry 4.0 in the areas of digital transformation and automation. In the context of the required rapid transformation of today’s enterprises, it becomes extremely important to look for solutions that allow the use of the existing infrastructure, information, and energy, so as to minimize the negative impact of new technologies and the transformation process itself on the environment. The article presents an approach to modeling large and complex production systems with the use of distributed Petri net models allowing the use of the possessed IT infrastructure as consistent with the idea of sustainable development in the activities of enterprises. This eliminates two major problems that render traditional models unusable. The first is related to the difficulties in analyzing and verifying models of enormous size and infinite space of states. The second is related to the required computing power, if such analyzes are to be performed on one computing unit, which would force the producers to replace the IT infrastructure. For this purpose, modular Petri nets are introduced. Other benefits of modularization, such as smaller components that can be independently analyzed, are also presented in the paper. The proposed modular Petri net has been implemented in the proprietary GPenSIM software. The paper is complemented by a practical example of industrial modeling of production systems with automated guided vehicles (AGVs) using the Modular Model with Intelligent Petri Modules.