Stability criteria of hybrid control systems and applications

The basis of a new approach of hybrid systems, called the mathematical-heuristic modelling, and its applications in analysis, simulation and stability of hybrid control systems are presented. The mathematical-heuristic model of a high complexity system is a hybrid model including a continuous and/or a discrete simulation model (a differential and/or a discrete-time model), a discrete event simulation model and a heuristic and/or a fuzzy knowledge-based control model, as a part of a network of interconnected models. A theorem of compatibility between the mathematical and the fuzzy knowledge-based models, by using the method of complete induction, ensures the theoretical basis of simulation and control. Criteria of structural and asymptotic stability of hybrid control systems are presented. The stability criteria of hybrid control systems are useful in the simulation and control of actual systems and evaluation of their stability, i.e. a large scale hydrological system composed of a network of great lakes interconnected by canals and channels, by using a PC 486 or upgrade.