Generalized dissipation in hysteretic systems

We give a formal definition of dissipative systems that is considerably more general than earlier definitions. The measured output is irrelevant in this formulation. The key component of dissipation is an appropriate work rate. We also define cycle-dissipation and show how it can be used to obtain a suitable work rate. Using this idea, we propose a new work rate for the Preisach hysteresis model, and demonstrate dissipativity with respect to this rate. The Preisach model describes the dynamics of many "smart materials" such as shape memory alloys. This new type of dissipativity will be beneficial in the design of position controllers for SMA.