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.
Issue Section:
Technical Briefs
1.
Abou-Kandil
H.
Freiling
G.
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.
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.
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.
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.
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.
Chizeck
H. J.
Feng
X.
Loparo
K. A.
1991
, “Stability and Control of Discrete-Time Jump Linear Systems
,” Control Theory and Advanced Technology
, Vol. 7
, No. 2
, pp. 247
–270
.12.
Mariton, M., 1990, Jump Linear Systems in Automatic Control, New York and Basel.
13.
Pan
G.
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.
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.
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.
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