Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach

380

1

00

10

A

2

0.008

0

B

, , ,

, ,

2

0.1 1

00

A

0

1

L

1

0.002

0.002

B

1

M0.7 0.008,

20.5 0.02M.

Suppose the actual controller is with perturbations in

the form of (2b) and (2c) with parameters as

0.15

kL,

00.02

kM.

We wish to design a robust non-fragile state feedback

controller for this system such that the resulting closed-

loop system is asymptotically stable for all admissible

uncertainties and controller gain variations. By solving

LMI (7) using the Matlab LMI toolbox [24,25] with

0.7

, we obtain the following feasible solution:

12

2.48020.2958 , 7.1774,7.6242

0.295818.1199

70.82140.3 .

S

U

(14)

Therefore, by Theorem 3.1, we can see that the robust

non-fragile control problem is solvable. A desired state

feedback controller to solve this problem can be chosen

as

14.4699 117.8843K. (15)

5. Conclusion

In this paper, we have investigated the problem of robust

non-fragile control for a class of 2-D discrete uncertain

systems in the FMSLSS setting under state feedback gain

variations. Using the Lyapunov method, a criterion for

robust non-fragile control via state feedback is derived in

terms of LMI. Finally, a numerical example has been

presented to illustrate the effectiveness of the proposed

method.

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