In this paper, we study the problem of robust stabilization of discrete-time linear systems with Markovian jumping parameters (DTLSMJP) with norm bounded uncertainties. A sufficient condition guaranteeing te robust stability of the uncertain discrete-time linear systems with Markovian jumping parameters (UDTLSMJP) is presented, which is in terms of a set of coupled discrete-time algebraic Riccati inequalities (IEqs). Finally, a numerical example is given to show the potential of the proposed technique.

1.
Abou-Kandil
H.
,
Freiling
G.
, and
Jank
G.
,
1995
, “
On the Solution of Discrete-time Markovian Jump Linear Quadratic Control Problems
,”
Automatica
, Vol.
31
, No.
5
, pp.
765
768
.
2.
Arnold, L., and Wihstutz, V., 1986, “Lyapunov Exponents,” Lecture Notes in Mathematics, Springer-Verlag, N.Y., No. 1186.
3.
Benjelloun, K., and Boukas, E. K., 1995, “On the Stability of Linear System with Markovian Jumping Parameters,” IEEE Conference on Decision & Control, pp. 75–76, New Orleans.
4.
Blair
W. P.
, and
Sworder
D. D.
,
1975
, “
Feedback Control of a Class of Linear Discrete Systems with Jump Parameters and Quadratic Cost Criteria
,”
Int. J. Control
, Vol.
21
, No.
5
, pp.
833
841
.
5.
Boukas
E. K.
, and
Yang
H.
,
1995
, “
Stability of Discrete-Time Linear Systems with Markovian Jumping Parameters
,”
Mathematic Control Signals Systems
, Vol.
8
, pp.
390
402
.
6.
Chizeck
H. J.
,
Wilsky
A. S.
, and
Castanon
D.
,
1986
, “
Discrete-Time Markovian-Jump Linear Quadratic Optimal Control
,”
Int. J. Control
, Vol.
43
, No.
1
, pp.
213
231
.
7.
Costa
O. L. V.
,
1995
, “
Discrete-Time Coupled Riccati Equations for Systems with Markov Switching Parameters
,”
Journal of Mathematical Analysis and Applications
, Vol.
194
, pp.
197
216
.
8.
Costa
O. L. V.
,
1996
, “
Mean Square Stabilizing Solutions for Discrete-Time Coupled Algebraic Riccati Equations
,”
IEEE Transactions on Automatic Control
, Vol.
41
, No.
4
, pp.
593
598
.
9.
Graham, A., 1981, “Kronecker Products and Matrix Calculus with Applications,” Ellis Horwood Series, Mathematics and its Applications.
10.
Ji
Y.
, and
Chizeck
H. J.
,
1988
, “
Controllability, Observability and Discrete-Time Markovian-Jump Linear Quadratic Control
,”
Int. J. Control
, Vol.
48
, No.
2
, pp.
481
498
.
11.
Ji
Y.
, and
Chizeck
H. J.
,
Feng
X.
, and
Loparo
K. A.
,
1991
, “
Stability and Control of Discrete-Time Jump Linear Systems
,”
, Vol.
7
, No.
2
, pp.
247
270
.
12.
Mariton, M., 1990, Jump Linear Systems in Automatic Control, New York and Basel.
13.
Pan
G.
, and
Bar-Shalom
Y.
,
1996
, “
Stabilization of Jump Linear Gaussian Systems without Mode Observations
,”
Int. J. Control
, Vol.
64
, No.
4
, pp.
631
661
.
14.
Petersen
I. R.
, and
Hollot
C. V.
,
1986
, “
A Riccati Equation Approach to the Stabilization of Uncertain Linear Systems
,”
Automatica
, Vol.
22
, No.
4
, pp.
397
411
.
15.
Shi
P.
, and
Boukas
E. K.
,
1997
, “
H control for Markovian jumping linear systems with parametric uncertainty
,”
J. Optim. Theory Appli.
, Vol.
95
, No.
1
, pp.
75
99
.
16.
Sworder
D. D.
,
1969
, “
Feedback Control of a Class of Linear Systems with Jump Parameters
,”
IEEE Trans. Automat. Contr.
, Vol.
14
, pp.
9
14
.
17.
Wonham, W. M., 1971, “Random Differential Equations in Control Theory,” Probabilistic Methods in Applied Mathematics, Vol. 2, A. T. Beruche-Reid, ed., N.Y.
This content is only available via PDF.