Hybrid dynamical systems for memristor modelling an approach avoiding the terminal-state problem

Leon O. Chua introduced the memristor as the fourth circuit element to complete the set of fundamental passive two-terminal elements in 1971. For a long time it seemed as if memristors were just toys in the sandbox of network theorists. The situation abruptly changed in 2008 when scientists from HP reported on a nanoelectronic device which showed a memristive behaviour. Main hopes for new opportunities and circuit concepts in the transition to increasingly smaller integrated circuits are going to be related to this discovery. For an examination of these possibilities by means of simulation a large number of memristor models has been developed in recent years. A special property of the behavioural models of memristive nanoelectronic devices is the restricted range of internal state variables. A number of tricky solutions has been developed up to now to handle this problem. In this paper we present a straightforward solution for this problem within the framework of hybrid dynamical systems.