Switched Systems

This chapter is concerned with dynamical systems described by a combination of ordinary differential equations and discrete switching events. Although systems theory has traditionally focused on either continuous or discrete behavior, many (if not most) of the dynamical systems encountered in practice involve both types of dynamics. Important classes of such systems are provided by

networked control systems

, in which information shared by continuous subsystems is updated in a discrete fashion, and

embedded systems

, in which computer software interacts with physical devices.

Dynamical systems that are described by an interaction between continuous and discrete dynamics are usually called

hybrid systems

. The field of hybrid systems has a strong interdisciplinary flavor, and different communities have developed different viewpoints. One approach, favored by researchers in computer science, is to concentrate on studying the discrete behavior of the system, while the continuous dynamics are assumed to take a relatively simple form. Basic issues in this context include well-posedness, simulation, and verification. Many researchers in systems and control theory, on the other hand, tend to regard hybrid systems as continuous systems with switching and place a greater emphasis on properties of the continuous state. The main issues then become stability analysis and control synthesis. The book [18] provides a good overview of both of these perspectives.