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By Kirsch U., Kocvara M., Zowe J.

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Definition 5: The set of variables Xi of a class is composed of Xi = Xco_i  Xint_i  Xpb_i  Xim_i  Xext_i, where (Xext_i  Xco_i)  (Xext_i  Xint_i)  (Xext_i  Xpb_i)  (Xext_i  Xim_i)  (Xco_i  Xint_i)  (Xco_i  Xpb_i)  (Xco_i  Xim_i)  (Xint_i  Xpb_i)  (Xint_i  Xim_i)  (Xpb_i  Xim_i) = . Definition 6: Each image variable of Xim_z of a class Cz is associated with a public variable of Xpb_i of a class Ci (i z or izz): x x x Each variable of Xim_z is associated with a variable of Xz called In, where n is an integer number.

The continuous evolution is a function of the time (T). 20 Modelling and Analysis of Hybrid Supervisory Systems As for the predicate transition net, differential predicate transition net also has enabling conditions, called enabling functions. When a transition is enabled, it fires immediately. The firing of an enabled transition has priority over time evolution. Another element of the differential predicate transition net is the junction function. Junction functions are used to introduce discontinuities in the continuous variables and are similar to the actions of predicate transition net.

Xi is a set of variables (see Definition 5). Api associates a sub-set Xpk_i of variables of Xi with each place pk_i (see Definition 4). Aci associates an enabling function ek_i with each transition tk_i. The enabling function is a Boolean expression that has the variables of Xi as input parameters. Aji associates a junction function jk_i with each transition tk_i. The junction function determines the values of the variables of Xi after the transition firing, Xi(T+) = jk_i(Xi(T-)) (T+, T- are time instants immediately before and after the firing of transition tk_i).