 
Summary: Introduction to the Special Issue on Hybrid Systems
Hybrid systems contain two distinct types of components, subsystems with continuous dynamics and subsystems
with discrete dynamics that interact with each other. These systems typically contain variables or signals that
take values from a continuous set and also variables that take values from a discrete, typically finite set. These
continuous or discretevalued variables depend on independent variables such as time, which may also be
continuous or discrete; some of the variables may also be discrete event driven in an asynchronous manner.
Since the continuous and discrete dynamics coexist and interact with each other it is important to develop
models that accurately describe the dynamic behavior of such hybrid systems. In this way it will be possible to
develop control strategies that fully take into consideration the relation and interaction of the continuous and
discrete parts of the system. There are several reasons for using hybrid models to represent the dynamic behavior
of interest. Reducing complexity was and still is an important reason for dealing with hybrid systems, and this is
accomplished by incorporating models of dynamic processes at different levels of abstraction. For example a
thermostat typically sees a very simple, but adequate for the task in hand, model of the complex heat flow
dynamics. In another example, one may choose to work with sets of simpler equations (e.g. linear) and switch
among these simpler models in order to avoid dealing directly with a set of nonlinear equations. In recent years,
the widespread use of digital machines has made hybrid systems very common. Whenever a digital device
interacts with the continuous world, the behavior involves hybrid phenomena that need to be analyzed and
understood. Hybrid systems are central in the analysis and design of intelligent control systems with high
degrees of autonomy as they arise from the interaction of discrete planning algorithms and continuous control
algorithms. The investigation of hybrid systems is creating a new and fascinating discipline bridging control
