Cyber-Physical Systems

Analysis and Design of Cyber-Physical Systems 23

values when initialized nearby. For models of such systems given in terms of hybrid inclusions as in

Equations 1.19 and 1.20 and without inputs, stability is defined as follows:

AclosedsetA ⊂ R

n

is said to be Lyapunov stable if for each ε > 0 there exists δ > 0 such that

each maximal solution φ to the hybrid inclusion in Equations 1.19 and 1.20 without inputs and with

|φ(0, 0)|

A

≤ δ

satisfies

|φ(t, j)|

A

≤ ε

for all (t, j) ∈ dom φ.

The notion reduces to stability of a point when the set A is a singleton, and |·|

A

is the distance

to the point A. The general closed set A in the definition allows to study the