Model-Based Testing for Embedded Systems

Model-Based Testing of Hybrid Systems 403

3

2

1

0

2.5

1.5

0.5

y

–0.5

–1

–1.5 –1 –0.5 0 1 20.5 1.5 2.5

x

3

2

1

0

2.5

1.5

0.5

y

–0.5

–1

–1.5 –1 –0.5 0 1 20.5 1.5 2.5

x

FIGURE 14.11

Results obtained using the guided sampling method (left) and using the uniform sampling

method (right).

Example 2. This example is a linear system with a stable focus at the origin. Its dynamics is



˙x

˙y



=



−1 −1.9

1.9 −1



×



x

y



+



u

1

u

2



.

We let the dynamics be slightly perturbed by an additive input u. The state space is the

box B =[−3, −3] ×[3,3]. The input set U = {u ∈ R

2

|||u|| ≤ 0.2}. Figure 14.11 shows the

results obtained after 50,000 iterations. We can see that again the guided sampling method