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This study investigates the global asmptotic stabilisability of an n-dimensional quantised feedforward non-linear system. The system’s dynamics are assumed to be locally Lipschitz. So the ranges of the state variables are tightly related to the parameters of the quantisation procedure, that is, there exists coupling between quantisation and control. To save network transmission bandwidth, less quantisation bits (per sample) are preferred. In De Persis’ paper, n bits (per sample) are shown to be enough to stabilise the n-dimensional system by taking a time-invariant quantiser, which assigns 1 bit to each state variable (dimension). We design a time-varying quantiser and can globally stabilise the system with only 1 bit, instead of n bits. That single bit is assigned to the most ‘important’ state variable at each sampling instant, which yields the time-varying coupling among the quantisation errors of state variables besides the coupling between quantisation and control. Owing to the well-designed structure of our quantiser, we can place exponentially converging upper bounds on the quantisation errors of state variables and well handle both types of couplings, so that the global stability of the system is guaranteed with 1 bit. An example is used to demonstrate the effectiveness of the proposed quantiser.
References
-
-
1)
-
C. DePersis ,
A. Isidori
.
Stabilizability by state feedback implies stabilizability by encoded state feedback.
Syst. Control Lett.
,
249 -
258
-
2)
-
D. Liberzon
.
On stabilization of linear systems with limited information.
IEEE Trans. Autom. Control
,
2 ,
304 -
307
-
3)
-
E. Tian ,
D. Yue ,
X. Zhao
.
Quantised control design for networked control systems.
IET Control Theory Appl.
,
6 ,
1693 -
1699
-
4)
-
J. Hespanha ,
P. Naghshtabrizi ,
Y. Xu
.
A survey of recent results in networked control systems.
Proc. IEEE
,
1 ,
138 -
162
-
5)
-
G.C. Walsh ,
H. Ye ,
L.G. Bushnell
.
Stability analysis of networked control systems.
IEEE Trans. Control Syst. Technol.
,
438 -
446
-
6)
-
D. Liberzon ,
J. Hespanha
.
Stabilization of nonlinear systems with limited information feedback.
IEEE Trans. Autom. Control
,
6 ,
910 -
915
-
7)
-
L. Qiang ,
M.D. Lemmon
.
Stability of quantised control systems under dynamic bit assignment.
IEEE Trans. Autom. Control
,
734 -
740
-
8)
-
R.W. Brockett ,
D. Liberzon
.
Quantized feedback stabilization of linear systems.
IEEE Trans. Autom. Control.
,
7 ,
1279 -
1289
-
9)
-
A.R. Teel
.
On ℒ2 performance induced by feedbacks with multiple saturations.
ESAIM
,
225 -
240
-
10)
-
C. DePersis
.
n-bit stabilization of n-dimensional nonlinear systems in feedforward form.
IEEE Trans. Autom. Control
,
3 ,
299 -
311
-
11)
-
M. Krstic
.
Feedback linearizability and explicit integrator forwarding controllers for classes of feedforward systems.
IEEE Trans. Autom. Control
,
10 ,
1668 -
1682
-
12)
-
Q. Ling ,
M.D. Lemmon ,
H. Lin
.
Asymptotic stabilization of dynamically quantized nonlinear systems in feedforward form.
J. Control Theory Appl.
,
1 ,
27 -
33
-
13)
-
C. DePersis
.
Minimal data rate control of nonlinear systems over networks with large delays.
Int. J. Robust Nonlinear Control
,
10 ,
1097 -
1111
-
14)
-
G.N. Nair ,
R.J. Evans
.
Exponential stabilisability of finite-dimensional linear systems with limited data rates.
Automatica
,
4 ,
585 -
593
-
15)
-
S. Tatikonda ,
S. Mitter
.
Control under communication constraints.
IEEE Trans. Autom. Control
,
7 ,
1056 -
1068
-
16)
-
G.N. Nair ,
R.J. Evans ,
I.M.Y. Mareels ,
W. Moran
.
Topological feedback entropy and nonlinear stabilization.
IEEE Trans. Autom. Control
,
9 ,
1585 -
1597
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2011.0530
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