Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
3.1 Systems Under Consideration
3.1 Systems Under Consideration
We consider multiple input, single output nonlinear systems as in Section 2.4. We properly
define all the constants: �
dx
dt
y
=
=
A (u) x + b (x, u)
C (u) x
(3.2)
where x (t) ∈ X ⊂ Rn , X compact, y (t) ∈ R, and u(t) ∈ Uadm ⊂ Rnu is bounded for all times.
The matrices A (u) and C (u) are:
⎛
0
⎜
A(u) = ⎜
.
⎝
a2 (u)
0
0
a3 (u)
. ..
· · ·
. ..
. ..
0
⎞
0
⎟
. ⎟
0 ⎟ ,
⎟
an (u) ⎠
0 · · · 0
C (u) = � a1 (u) 0 · · · 0 � ,
with3 0