A NEW APPROACH TO DISCRETE-EVENT DYNAMIC SYSTEM THEORY

Abstract

The paper presents an original formulation of discrete-event dynamic systems (DEDS) strictly consistent with the Kalman definition of dynamic systems. The paper starts with a clear definition of event as a pair (occurrence time, fact), where the time is a real number and the fact is an element of a set with algebraic properties. The introduction of the concept of event sequences and of suitable operations over their set allows to formulate DEDS as causal operators transforming input e\'ent sequences into output event sequences. The definition of a state for such operator allows to give a state representation of the input-output relation. The state representation is a state equation as in the standard continuous or discrete-time systems, and allows to compute the free and the forced responses of the system. The paper terminates by providing the elementary stability defmitions and the state equations of linear and time-invariant DEDS.