Abstract

This paper discusses the problem of positive real control for uncertain 2-D linear discrete time singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainty. The purpose of this study is to design a state feedback controller such that the resulting closed-loop system is acceptable, jump modes free and stable, and achieves the extended strictly positive realness for all admissible uncertainties. A version of positive real lemma for the 2-D SRM is given in terms of linear matrix inequalities (LMIs). Based on the lemma, a sufficient condition for the solvability of the positive real control problem is derived in terms of bilinear matrix inequalities (BMIs) and an iterative procedure for solving the BMIs is proposed.

주제어

#2-D singular systems   #positive real control   #positive realness   #LMIs   #state feedback  

저자의 다른 논문

참고문헌 (26)

1. C. Cai, W. Wang, and Y. Zou. 'A note on the internal stability for 2-D acceptable linear singular discrete systems,' Accepted by Multidimensional Systems & Signal Processing 
2. W. Wang and Y. Zou, 'The detectability and observer design of 2-D singular systems,' IEEE Trans. on Circuits & Systems, vol. 49, no. 5, pp. 698-703, 2002 
3. W. M. Haddad and D. S. Bernstein, 'Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. part II: discrete-time theory,' International Journal of Robust Nonlinear Control, vol. 4, pp. 249-265, 1994 
4. L. Zhang, J. Lam, and S. Xu, 'On positive realness of descriptor systems,' IEEE Trans. on Circuits & Systems-I: Fundamental Theory and Applications, vol. 49, no. 3, pp. 401-407, 2002 
5. T. Kaczorek, 'The singular general model of 2-D systems and its solutions,' IEEE Trans. on Automatic Control, vol. 33, no. 11, pp. 1060- 1061, 1988 
6. H. Xu, Y. Zou, S. Xu, and J. Lam, 'Bounded real lemma and robust $H_\infty$ control of 2-D singular Roesser models,' Submitted to Systems & Control Letters 
7. M. S. Mahmoud and L. Xie, 'Positive real analysis and synthesis of uncertain discrete time systems,' IEEE Trans. on Circuits & Systems, vol. 47, no. 3, pp. 403-406, 2000 
8. W. Sun, P. P. Khargonekar, and D. Shim, 'Solution to the positive real control problem for linear time-invariant systems,' IEEE Trans. on Automatic Control, vol. 39, no. 10, pp. 2034- 2046, 1994 
9. D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou, 'A new robust D-stability condition for real convex polytopic uncertainty,' Systems & Control Letters, vol. 40, pp. 21-30, 2000 
10. Y. Zou and S. L. Campbell, 'The jump behavior and stability analysis for 2-D singular systems,' Multidimensional Systems & Signal Processing, vol. 11, pp. 321-338, 2000 
11. P. Molander and J. C. Willems, 'Synthesis of state feedback control laws with a specified gain and phase margin,' IEEE Trans. on Automatic Control, vol. 25, no. 5, pp. 928-931, 1980 
12. S. Xu and J. Lam, 'Positive real control of uncertain singular systems with state delay,' Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms, vol. 9, pp. 387-402, 2002 
13. Y. Zou, W. Wang, and S. Xu, 'Structural stability of 2-D singular systems Part II: a lyapunov approach,' Proc. of the Fourth International Conference on Control and Automation, Montreal, Canada, June, 2003 
14. B. D. O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis: A Modern System Theory Approach, Prentice-Hall, Upper Saddle River, NJ, 1973 
15. W. M. Haddad and D. S. Bernstein, 'Robust stabilization with positive real uncertainty: beyond the small gain theorem,' Systems & Control Letters, vol. 17, pp. 191-208, 1991 
16. T. Kaczorek, 'Acceptable input sequences for singular 2-D linear systems,' IEEE Trans. on Automatic Control, vol. 38, no. 9, pp. 1391-1394, 1993 
17. Y. Zou, W. Wang, and S. Xu, 'Regular state observers design for 2-D singular Roesser models,' Proc. of the Fourth International Conference on Control and Automation, Montreal, Canada, June, 2003 
18. M. S. Mahmoud, Y. C. Soh, and L. Xie, 'Observer-based positive real control of uncertain linear systems,' Automatica, vol. 35, pp. 749-754, 1999 
19. C. Du and L. Xie, $H_\infty$ Control and Filtering of Two-dimensional Systems, Springer-Verlag, Berlin, 2002 
20. Y. Zou, W. Wang, and S. Xu, 'Structural stability of 2-D singular systems-Part I: basic properties,' Proc. of the Fourth International Conference on Control and Automation, Montreal, Canada, June, 2003 
21. T. Kaczorek, 'General response formula and minimums energy control for the general singular model for 2-D systems,' IEEE Trans. on Automatic Control, vol. 35, no. 4, pp. 433- 436, 1990 
22. S. Xu, J. Lam, and C. Yang, 'Robust $H_\infty$ control of uncertain discrete singular systems with pole placement in a disk,' Systems & Control Letters, vol. 43, pp. 85-93, 2001 
23. M. Vidyasagar, Nonlinear Systems Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1993 
24. A. V. Karamanciogle and F. R. Lewis, 'Geometric theory for singular Roesser model,' IEEE Trans. on Automatic Control, vol. 37, no. 6, pp. 801-806, 1992 
25. T. Kaczorek, Two-Dimension Linear Systems, Spring-Verlag, New York ,1985 
26. T. Kaczorek, 'The linear-quadratic optimal regulator for singular 2-D systems with variable coefficients,' IEEE Trans. on Automatic Control, vol. 34, no. 5, pp. 565-566, 1989 

이 논문을 인용한 문헌 (0)

1. 이 논문을 인용한 문헌 없음