A mixed-Boolean hybrid mathematical model with discontinuous states

Hybrid mathematical models typically have discontinuous inputs, or are visualised as state machines or pertri-nets comprising continuous models linked by discontinuous mappings. The analysis and simulation of hybrid (or nonsmooth dynamical) models is plagued with difficulty, necessitating careful consideration of energy losses and state reinitialisation on commutation. The author proposes and alternative model, where states are discontinuous. The engineer familiar with techniques such as signal flow graphs or bond graphs can clearly visualise discontinuities as breaks (or joins) in power flow between parts of the model. A mixed-Boolean state equation can be derived which reflects the physics of switching behaviour. This has two advantages: it can be simulated without the need for state reinitialisation algorithms, and it can be analysed for structural control properties to show how they change with commutation.