Discrete and Hybrid State System Modeling and Analysis

Abstract

Classical modeling of physical systems relies on differential-difference type equations. However many systems todey cnotain logical quantities and discrete decision makers. For example, a robot can be modeled by differential equations but the task of the robot or how to accomplish that task requires dealing with logic (discrete) variables. We develop a discrete and hybrid state system formulation to study systems with both discrete and continuous quantities. We provide some analysis methods for hybrid state systems. We investigate classical Lyapunov stability of a continuous state in a hybrid state system configuration. Furthermore, we consider two examples of hybrid state systems.