Robust stabilization of discrete-time nonlinear Lur'e systems with sector and slope restricted nonlinearities

Applied Mathematics and Computation

Volumn 200, Issue 1, 2008, Pages 429-436

  Lee, S M ^a   Park, Ju H ^b  

^a KT Cooperation   (South Korea)

^b Yeungnam University   (South Korea)

Author keywords

LMIs; Lur'e systems; Sector and slope bound

Indexed keywords

CONSTRAINT THEORY; DISCRETE TIME CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; STABILIZATION; STATE FEEDBACK; UNCERTAIN SYSTEMS;

LUR'E SYSTEMS; SECTOR RESTRICTED NONLINEARITIES; SLOPE RESTRICTED NONLINEARITIES;

NONLINEAR SYSTEMS;

EID: 43049164440     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.11.031     Document Type: Article

References (18)

1. Lur'e A.I., and Postnikov V.N. On the theory of stability of control systems. Prikl. Mat. Mekh. 8 3 (1944)
2. Vidyasagar M. Nonlinear System Analysis. second ed. (1993), Prentice Hall, Englewood Cliffs, NJ
3. Khalil H.K. Nonlinear Systems. second ed. (1996), Prentice Hall
4. Sun J., Zhang Y., Wang L., and Wu Q. Impulsive robust control of uncertain Lure systems. Phys. Lett. A 304 (2002) 130-135
5. Liu B., Chen G., Teo K.L., and Liu X. Robust global exponential synchronization of general Lur'e chaotic systems subject to impulsive disturbances and time delays. Chaos, Solitons & Fractals 23 (2005) 1629-1641
6. Haddad W.M., and Kapila V. Absolute stability criteria for multiple slope-restricted monotonic nonlinearities. IEEE Trans. Automat. Contr. 40 (1995) 361-365
7. Singh V. A stability inequality for nonlinear feedback systems with slope-restricted nonlinearity. IEEE Trans. Automat. Contr. AC-29 (1984) 743-744
8. Suykens J.A.K., Vandewalle J., and Moor B.D. An absolute stability criterion for the Lur'e problem with sector and slope restricted nonlinearities. IEEE Trans. Circuits Syst. 45 (1998) 1007-1009
9. Park P. Stability criteria of sector- and slope-restricted Lur'e systems. IEEE Trans. Automat. Contr. 47 (2002) 308-313
10. Scherer C. A full block s-procedure with applications. IEEE Conf. Decis. Contr. (1997) 2602-2607
11. Skelton R.E., Iwasaki T., and Grigoriadis K.M. A Unified Algebraic Approach to Linear Control Design (1997), Taylor and Francis, New York
12. Johansson R., and Robertsson A. Observer-based strict positive real (SPR) feedback control system design. Automatica 38 (2002) 1557-1564
13. Arcak M., and Kokotovic P. Observer-based control of systems with slope-restricted nonlinearities. IEEE Trans. Automat. Contr. 46 (2001) 1146-1150
14. Hsu K.C. Variable structure control design for uncertain dynamic systems with sector nonlinearities. Automatica 34 (1998) 505-508
15. Hsu K.C., Wang W.Y., and Lin P.Z. Sliding mode control for uncertain nonlinear systems with multiple inputs containing sector nonlinearities and deadzones. IEEE Trans. Systems, Man and Cybernetics - Part B: Cybernetics 34 (2004) 374-380
16. Park P.G., and Kim S.W. A revisited Tsypkin criterion for discrete time nonlinear Lur'e systems with monotonic sector-restrictions. Automatica 34 (1998) 1417-1420
17. C. Scherer, S. Weiland, Lecture Notes on Linear Matrix Inequalities in Control, 2005.
18. Boyd S., Ghaoui L.E., Feron E., and Balakrishnan V. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadelphia, PA