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In this study, the authors focus on the controllability and observability of switched linear systems composed by continuous-time and discrete-time subsystems. Necessary and sufficient conditions for controllability and observability are obtained. A simple example is proposed to illustrate the effectiveness of the current theoretical results.
References
-
-
1)
-
D. Liberzon
.
(2003)
Switching in systems and control.
-
2)
-
K.S. Narendra ,
J. Balakrishnan
.
Adaptive control using multiple models.
IEEE Trans. Autom. Control
,
2 ,
171 -
187
-
3)
-
S.S. Ge ,
Z. Sun ,
T.H. Lee
.
Reachability and controllability of switched linear discrete-time systems.
IEEE Trans. Autom. Control
,
1437 -
1441
-
4)
-
D. Zhao ,
J.-L. Wang
.
Robust static output feedback design for polynomial nonlinear systems.
Int. J. Robust Nonlinear Control
,
1637 -
1654
-
5)
-
D.P. Stanford
.
Stability for a multi-rate sampled-data system.
SIAM J. Control Optim.
,
390 -
399
-
6)
-
McClamroch N.H. Kolmanovsky
.
Hybrid feedback laws for a class of cascade nonlinear control systems.
IEEE Trans. Autom. Control
,
1271 -
1282
-
7)
-
T. Yang
.
(2001)
Impulsive control theory.
-
8)
-
Z. Sun
.
Reachability analysis of constrained switched linear systems.
Automatica
,
164 -
167
-
9)
-
Zhai, G., Lin, H., Michel, A.N.: `Stability analysis for switched with continuous-time and discrete-time subsystems', Proc. American Control Conf., 2004, p. 4555–4560.
-
10)
-
Z. Sun ,
S.S. Ge
.
(2005)
Switched linear system-control and design.
-
11)
-
Z. Sun ,
S.S. Ge ,
T.H. Lee
.
Controllability and reachability criteria for switched linear systems.
Automatica
,
775 -
786
-
12)
-
G. Xie ,
D. Zheng ,
L. Wang
.
Controllability of switched linear systems.
IEEE Trans. Autom. Control
,
1401 -
1405
-
13)
-
H.J. Chizeck ,
A.S. Willsky ,
D. Castanon
.
Discrete-time Markovian jump linear quadratic optimal control.
Int. J. Control
,
213 -
231
-
14)
-
L.T. Conner ,
D.P. Stanford
.
State deadbeat response and observability in multi-modal systems.
SIAM J. Control Optim.
,
630 -
644
-
15)
-
Z. Yang
.
An algebraic approach towards the controllability of controlled switching linear hybrid systems.
Automatica
,
7 ,
1221 -
1228
-
16)
-
C.-T. Chen
.
(1988)
Linear system theory and design.
-
17)
-
G. Zhai ,
D. Liu ,
J. Imae
.
Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems.
IEEE Trans. Circuits Syst.
,
152 -
156
-
18)
-
S. Zhao ,
J. Sun
.
Controllability and observability for impulsive systems in complex fields.
Nonlinear Anal. RWA
,
3 ,
1513 -
1521
-
19)
-
Zhu, Y., Xing, J., Guan, Z.: `Controllability of switched systems with continuous-time and discrete-time subsystems', Seventh World Congress Intelligent Control Automation 2008, 2008, p. 4116–4119.
-
20)
-
Z. Sun ,
S.S. Ge
.
Analysis and synthesis of switched linear control systems.
Automatica
,
181 -
195
-
21)
-
Z. Ji ,
L. Wang ,
X. Guo
.
On controllability of switched linear systems.
IEEE Trans. Autom. Control
,
796 -
801
-
22)
-
G. Zhai ,
X. Xu ,
H. Lin
.
Extension of Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems.
Int. J. Appl. Math. Comput. Sci.
,
447 -
454
-
23)
-
G. Xie ,
L. Wang
.
Reachability realization and stabilizability of switched linear discrete-time systems.
J. Math. Anal. Appl.
,
209 -
220
-
24)
-
W.L. Brogan
.
(1991)
Modern control theory.
-
25)
-
Brockett, R.W., Wood, J.R.: `Electrical networks containing controlled switches. Applications of Lie group theory to nonlinear network problems', Supplement to IEEE Int. Symp. Circuit Theory, 1974, San Francisco, CA, p. 1–11.
-
26)
-
D. Gomez-Gutierrez ,
G. Ramirez-Prado ,
A. Ramirez-Trevino
.
Observability of switched linear systems.
IEEE Trans. Ind. Inf.
,
127 -
135
-
27)
-
B. Liu ,
H.J. Marquez
.
Controllability and observability for a class of controlled switching impulsive systems.
IEEE Trans. Autom. Control
,
2360 -
2366
-
28)
-
S.W. Zhao ,
J.T. Sun
.
A geometric approach for reachability and observability of linear switched impulsive systems.
Nonlinear Anal.
,
4221 -
4229
-
29)
-
D.D. Sworder
.
Control of systems subject to sudden changes in character.
Proc. IEEE
,
1219 -
1225
-
30)
-
W.M. Leonessa ,
Chellaboina V. Haddad
.
Nonlinear system stabilization via hierarchical switching control.
IEEE Trans. Autom. Control
,
17 -
28
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