Robust Finite-time Dissipative State Feedback Controller Design for Discrete-time Uncertain Singular Systems

- Journal title : The Transactions of The Korean Institute of Electrical Engineers
- Volume 64, Issue 11, 2015, pp.1598-1604
- Publisher : The Korean Institute of Electrical Engineers
- DOI : 10.5370/KIEE.2015.64.11.1598

Title & Authors

Robust Finite-time Dissipative State Feedback Controller Design for Discrete-time Uncertain Singular Systems

Kim, Jong Hae; Oh, Do Chang;

Kim, Jong Hae; Oh, Do Chang;

Abstract

In this paper, we treat the problem of a robust finite-time dissipative state feedback controller design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for finite-time stability of discrete-time singular systems is derived. A finite-time dissipative state feedback controller design method satisfying finite-time stability and dissipativity is proposed by LMI(linear matrix inequality) technique on the basis of the obtained BRL. Moreover it is shown that the obtained condition can be extended into polytopic uncertain systems by proper manipulations. Finally, illustrative examples are given to show the applicability of the proposed method.

Keywords

Robust dissipativity;Finite-time control;Uncertainty;Discrete-time singular systems;

Language

Korean

References

1.

G. Kamenkov, "On stability of motion over a finite interval of time," Journal of Applied Math and Mechanics, PMM, vol. 17, pp. 529-540, 1953.

2.

P. Dorato, An overview of finite-time stability, Current Trends in Nonlinear Systems and Control, Birkhauser, Boston, pp. 185-194, 2006.

3.

F. Amato, R. Ambrosino, M. Ariola, C. Cosentino, and G. D. Tommasi, Finite-time stability and control, Lecture Notes in Control and Information Sciences 453, Springer, London, 2014.

4.

C. Liu, Y. Zhang, and H. Sun, "Finite-time $H_{\infty}$ filtering for singular stochastic systems," Journal of Applied Mathematics, Hindawi Publishing Corp., vol. 2012, ID 615790, 2012.

5.

J. LaSalle and S. Lefschetz, Stability by Liapunov's direct method, Academic Press, New York, 1961.

6.

C. I. Byrnes, A. Isidori, and J. C. Willems, "Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems," IEEE Trans. on Automatic Control, vol. 36, no. 11, pp. 1228-1240, 1991.

7.

N. Kottenstette and P. J. Antsaklis, "Relationship between positive real, passive dissipative, and positive systems," Proc. of American Control Conference, Baltimore, MD, USA, pp. 409-416, 2010.

8.

C. Li and X. Liao, "Passivity analysis of neural networks with time delay," IEEE Trans. Circuits and Systems-II, Exp. Briefs, vol. 52, no. 8, pp. 471-475, 2005.

9.

L. Xie, M. Fu, and H. Li, "Passivity analysis and passification for uncertain signal processing systems," IEEE Trans. Signal Process., vol. 46, no. 9, pp. 2394-2403, 1998.

10.

D. Q. Wei and X. S. Luo, "Passivity-based adaptive control of chaotic oscillations in power systems," Chaos Solitons Fractals, vol. 31, no. 3, pp. 665-671, 2007.

11.

Q. Li, Q. Zhang, N. Yi, and Y. Yuan, "Robust passive control for uncertain time-delay singular systems," IEEE Trans. Circuits and Systems-I, Reg. Papers, vol. 56, no. 3, pp. 653-663, 2009.

12.

A. Ling, Y. Hui, and D. X. Zhuang, "Passive control for uncertain discrete time-delay singular systems," Proc. 3rd International Conf. on Intelligent Networks and Intelligent Systems, pp. 156-159, 2010.

13.

H. Li and S. Shi, "Robust passive control for singular systems with time-delay and uncertainties," Proc. International Conf. on Electronic and Mechanical Engineering and Information Technology, pp. 4853-4855, 2011.

14.

Z. Feng, J. Lam, and H. Gao, "${\alpha}$ -dissipativity analysis of singular time-delay systems," Automatica, vol. 47, pp. 2548-2552, 2011.

15.

X. M. Zhang and Q. L. Han, "Delay-dependent robust $H_{\infty}$ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality," IEEE Trans. Circuits and Systems-II, vol. 53, pp. 1466-1470, 2006.

16.

F. Amato, M. Ariola, and Cosentino, "Finite-time control of discrete-time linear systems: analysis and design conditions Finite-time output feedback control of discrete-time systems," Automatica, vol. 46, pp. 919-924, 2010.

17.

S. Wo and X. Han, "Finite-time stability analysis of discrete-time linear singular systems," Journal of Applied Mathematics, Hindawi Publishing Corp., vol. 2014, ID 579863, 2014.

18.

S. B. Stojanovic, D. L. J. Debeljkovic, and D. S. Antic, "Finite-time stability and stabilization state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional," Bulletin of the polish academy of sciences technical sciences, vol. 63, no. 2, pp. 479-487, 2015.

19.

D. S. Antic, S. B. Stojanovic, and D. L. J. Debeljkovic, "Finite-time stability and stabilization of singular discrete time-delay systems," XI International SAUM Conference on Systems, Automatic Control and Measurements, Serbia, pp. 160-163, 2012.

20.

Y. Ma, L. Fu, Y. Jing, and Q. Zhang, "Finite-time $H_{\infty}$ control for a class of discrete-time switched singular time-delay systems subject to actuator saturation," Applied Mathematics and Computation, vol. 261, pp. 264-283, 2015.

21.

L. Dai, Singular control Systems, Berlin, Springer-Verlag, 1989.

22.

E. M. N. Lopez, "Several dissipativity and passivity implications in the linear discrete-time setting," Mathematical Problems in Engineering, vol. 6, pp. 599-616, 2005.