... point of Nyquist plot of the equalized system
and the critical point –1.
500 Analysis and Control of Linear Systems
a) Robustness of stability
b) Robustness of performance
Figure 15. 10. ...
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
22
22
11
11
9.1
1.0
9.1
2
KK
KK
KK
KK
KK
KK
DC
BA
DC
BA
DC
BA
δδ
[15. 80]
512 Analysis and Control of Lin...
...
2 a
n-1
a
n-3
a
n-5
…
3 b
1
=a
n-2
-a
n
a
n-3
/a
n-1
b
2
=a
n-4
-a
n
a
n-5
/a
n-1
b
3
=a
n-6
-a
n
a
n-7
/a
n-1
…
4 c
1
=a
n-3
-b
2
a
n-1
/b
1
c
2
=a
n-5
-b
3
a
n-1
/b
1
...
study the case of open loop stable systems, that of integrator systems and finally the
case of open loop unstable systems.
270 Analysis and Control of Linear Systems
We...
... order 493
15. 2. The µ -analysis 493
15. 2.1. Analysis diagram and structured single value 495
15. 2.2. Main results of robustness 495
15. 2.3. Example 496
vi Analysis and Control of Linear Systems ... Congress Cataloging-in-Publication Data
[Analyse des systèmes linéaires/Commande des systèmes linéaires. eng] Analysis and control
of linear systems anal...
... values of
ξ
.
10
0
-1 0
-2 0
-3 0
0
-4 5
-9 0
-1 35
-1 80
1
T
1
1
T
2
Module (dB)Phase (degree)
Figure 1.23. Bode diagram of a second order system with
ξ
≥
1
20 Analysis and Control of Linear Systems ... of Linear Systems
Figure 1.19. Unit-step response of the second order system
ξ
≥
1
1=
ξ
: critical state. The roots of the deno...
...
104 Analysis and Control of Linear Systems
Figure 3.5. Bode diagram of the continuous system and its discretization
3.4.5. The problem of sub-sampling
Let us consider the case of a “standardized” ... polynomial of an order equal to 1−
i
n , where
i
n is the
multiplicity order of
i
λ
and i
th
the eigenvalue of A.
5 A canonical form called controllable...
... eigenvalues of A appear (certain powers l
ij
being
then equal to 0):
110 Analysis and Control of Linear Systems
The object of this chapter is to describe certain structural properties of linear
systems ... and
intersection of sub-spaces (the sum and intersection of two A-invariant sub-spaces
are A-invariant). Consequently, for any
L ⊂ X sub-space, there...
... 144 Analysis and Control of Linear Systems
On the other hand, the Fourier transform preserves the energy (Parseval theorem).
Indeed, the energy of a continuous-time signal y(t) or of a discrete-time ... proximity of ν
0
.
142 Analysis and Control of Linear Systems
A discrete-time deterministic signal y[k],k ∈Zis, by definition, a sequence of
complex numbers:
y =...
... the condition of detectability by a careful choice of matrix Q.
162 Analysis and Control of Linear Systems
case of multi -control systems. As indicated in Chapter 2, the equations of state can ... at the expense of a stronger control.
176 Analysis and Control of Linear Systems
Figure 6.6. Stabilization by quadratic optimization
166 Analysis a...
... from the point of view
of calculation, in terms of linear regression (or linearized), i.e. it leads to a quadratic
196 Analysis and Control of Linear Systems
in performing the roles of the procedure, ... [7.44]
Two parameters must be identified: the static gain of system K and the time con-
stant τ.
216 Analysis and Control of Linear Systems
so-called “sha...
... order, the
242 Analysis and Control of Linear Systems
Consequently, the field of absolute stability of multi-interval methods (implicit or
not depending on the value of β
0
) is the set of µ ∈ C so ... desired and to perform the corre-
sponding substitutions. Let us take the example of the classic PID regulator. Let e(t)
230 Analysis and Control of Linear Sys...