For many purposes, especially in the context of control systems analysis and design, both the process under consideration and the specifications to be met can be adequately modeled by discrete event or hybrid systems. A discrete event system (DES) describes the occurrence of certain selected events, for example the crossing of well-defined threshold values by temperature or pressure variables. If only the temporal order of events is important, a logical discrete event system is an appropriate choice. Logical DES can be formulated as (finite) automata, formal languages, Petri nets etc.

If additional time information, other than ordering, is important for judging the correct functioning of the respective process, timed DES must be used. Examples are timed automata, timed Petri nets, and the so-called Max-plus-algebra. A model containing both discrete event components and continuous dynamics with nontrivial interaction is called hybrid. Hybrid models are ubiquitous in modern control systems, where discrete control functions influence, and are influenced by, continuous plant and controller dynamics.