Discrete Time Systems with Event-Based Dynamics: Recent Developments in Analysis and Synthesis Methods

In this chapter we considered discrete event systems within the paradigm of algebraic state space models. As we pointed out, traditional approaches to system analysis and controller synthesis that were developed for continuous and discrete time dynamical systems may not be suitable for the same or similar tasks in the case of discrete event systems. Thus, one of the main challenges in the field of discrete event systems is the development of appropriate mathematical techniques. Finding new mathematical indicators that characterize the dynamic properties of a discrete event system represents a promising approach to the development of new analysis and controller synthesis methods.