ABSTRACT
Such systems are particularly interesting when they consist of interconnected components forming a flow network. The output of a node in such a network can become the input of one or more other nodes. Moreover, controls may be applied (e.g., valves) to regulate the amount of flow allowed in/out of various nodes so as to achieve desired
specifications. The hybrid nature of such systems is seen in (6.1) where the events “x(t) reaches/leaves 0” or “x(t) reaches/leaves C” cause a switch in the operating mode of the system. Similar switches may occur as a result of controllable events such as “shut down the outgoing flow” or uncontrollable ones such as “incoming flow changes from one constant value to another.” The dynamics become stochastic when α(t) and β (t) are random processes, normally assumed to be independent of each other.
