© The Institution of Engineering and Technology
A class of extended continuous-time Markov jump linear systems is proposed in this study. The generality lies in that the discrete dynamics of the class of systems is described by a Markov stochastic process, but with only partially known transition probabilities, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be known a priori. Moreover, in contrast with the uncertain transition probabilities studied recently, no structure (polytopic ones), bounds (norm-bounded ones) or ‘nominal’ terms (both) are required for the partially unknown elements in the transition rate matrix. The sufficient conditions for H∞ control are derived via the linear matrix inequality formulation such that the closed-loop system is stochastically stable and has a guaranteed H∞ noise-attenuation performance. A tradeoff can be built using our approach between the difficulties to obtain all the transition probabilities and the systems performance benefits. A numerical example is provided to show the validity and potential of the developed theoretical results.
References
-
-
1)
-
L. Zhang ,
P. Shi ,
E.K. Boukas ,
C. Wang
.
H∞ control of switched linear discrete-time systems with polytopic uncertainties.
Optim. Control Appl. Meth
,
5 ,
273 -
291
-
2)
-
J. Daafouz ,
P. Riedinger ,
C. Iun
.
Stability analysis and control synthesis for switched systems: a switched lyapunov function approach.
IEEE Trans. Autom. Control
,
11 ,
1883 -
1887
-
3)
-
Y. Wang ,
Z. Sun
.
H∞ control of networked control system via LMI approach.
Int. J. Innov. Comput., Inf. Control
,
2 ,
343 -
352
-
4)
-
L. Zhang ,
E. Boukas ,
J. Lam
.
Analysis and synthesis of markov jump linear systems with time-varying delays and partially known transition probabilities.
IEEE Trans. Automat. Control
,
10 ,
2458 -
2464
-
5)
-
X. Feng ,
K.A. Loparo ,
L. Ji ,
H.J. Chizeck
.
Stochastic stability properties of jump linear systems.
IEEE Trans. Autom. Control
,
38 -
53
-
6)
-
V. Zakian
.
(2005)
Control systems design: a new framework.
-
7)
-
D. Liberzon
.
(2003)
Switching in systems and control.
-
8)
-
E. Inohira ,
T. Uoi ,
H. Yokoi
.
Generalization capability of neural networks for generation of coordinated motion of a hybrid prosthesis with a healthy arm.
Int. J. Innov. Comput. Inf. Control
,
2 ,
471 -
484
-
9)
-
E.K. Boukas
.
(2005)
Stochastic switching systems: analysis and design.
-
10)
-
U. Shaked
.
Improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty.
IEEE Trans. Automat. Control
,
4 ,
652 -
656
-
11)
-
Y. Ji ,
H.J. Chizeck
.
Controllability, stabilisability, and continuous-time Markovian jump linear quadratic control.
IEEE Trans. Autom. Control
,
777 -
788
-
12)
-
L. Zhang ,
Y. Shi ,
T. Chen ,
B. Huang
.
A new method for stabilization of networked control systems with random delays.
IEEE Trans. Autom. Control
,
8 ,
1177 -
1181
-
13)
-
C.E. De Souza ,
A. Trofino ,
K.A. Barbosa
.
Mode-independent H∞ filters for Markovian jump linear systems.
IEEE Trans. Automat. Control
,
11 ,
1837 -
1841
-
14)
-
P. Seiler ,
R. Sengupta
.
An H∞ approach to networked control.
IEEE Trans. Autom. Control
,
3 ,
356 -
364
-
15)
-
M. Karan ,
P. Shi ,
C.Y. Kaya
.
Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems.
Automatica
,
12 ,
2159 -
2168
-
16)
-
O.L.V. Costa ,
M.D. Fragoso ,
R.P. Marques
.
(2005)
Discrete-time Markovian jump linear systems.
-
17)
-
X. Zhong ,
H. Xing ,
K. Fujimoto
.
Sliding mode variable structure control for uncertain stochastic systems.
Int. J. Innov. Comput., Inform. Control
,
2 ,
397 -
406
-
18)
-
J. Xiong ,
J. Lam ,
H. Gao ,
D.W.C. Ho
.
On robust stabilization of markovian jump systems with uncertain switching probabilities.
Automatica
,
5 ,
897 -
903
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2008.0023
Related content
content/journals/10.1049/iet-cta.2008.0023
pub_keyword,iet_inspecKeyword,pub_concept
6
6