Linear Hybrid Dynamical Systems

Abstract

Hybrid dynamical systems are systems that combine continuous dynamics and discrete events. In practice, hybrid systems arise when some parts of a physical system can be modeled by differential equations while other parts are more conveniently described by logic or discrete-event systems. A simple example is a continuous process controlled by switching logic (implemented by, say, a programmable logic controller). Although the piecewise linear systems considered so far can be regarded as hybrid systems (the cell index can be seen as a discrete state variable whose value changes when the continuous state crosses a cell boundary) the discrete state has a very passive role in this case, and this model class exhibits few behaviors that cannot be understood using standard nonlinear systems theory.