Section: Application Domains

Introduction

Many systems (either actual or abstract) can be represented by (1 ). Some typical examples are:

• Mechanical systems with unilateral constraints and dry friction (the biped robot is a typical example), including kinematic chains with slack, phenomena of liquid slosh, etc.

• Electrical circuits with ideal diodes and/or transistors Mos.

• Optimal control with constraints on the state, closed loop of a system controlled by an mpc algorithm(model predictive control), etc.

This class of models is not too large (to allow thorough studies), yet rich enough to include many applications. This goes in contrast to a study of general hybrid systems. Note for example that (1 ) is a “continuous” hybrid system, in that the continuous variables $x$ and $u$ prevail in the evolution (there is no discrete control to commute from a mode to the other: only the input $u$ can be used). Let us cite some specific applications.