Strongly absolute stability of Lur'e descriptor systems: Popov-type criteria

International Journal of Robust and Nonlinear Control

Volumn 19, Issue 7, 2009, Pages 786-806

  Yang, Chunyu ^a   Zhang, Qingling ^a,b   Zhou, Linna ^a  

^a KEY LABORATORY OF INTEGRATED AUTOMATION OF PROCESS INDUSTRY   (China)

^b NORTHEASTERN UNIVERSITY   (China)

Author keywords

Linear matrix inequality (lmi); Lur'e descriptor systems; Popov type criteria; Strongly absolute stability

Indexed keywords

ABSOLUTE STABILITY; COMPUTATIONAL ISSUES; DESCRIPTOR SYSTEMS; LINEAR MATRIX INEQUALITY (LMI); LUR'E DESCRIPTOR SYSTEMS; NUMERICAL EXAMPLE; POPOV-TYPE CRITERIA; STRONGLY ABSOLUTE STABILITY; SUFFICIENT CONDITIONS;

DESCRIBING FUNCTIONS; DIFFERENTIAL EQUATIONS; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STABILITY CRITERIA; TRAJECTORIES; UNCERTAIN SYSTEMS;

SYSTEM STABILITY;

EID: 67649232402     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1350     Document Type: Article

References (26)

1. Haddad WM, Bernstein DS. Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle and Popov theorems and their application to robust stability part i: continuous-time theory. International Journal of Robust and Nonlinear Control 1993; 3 (4) :313-339.
2. Haddad WM, Bernstein DS. 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 and Nonlinear Control 1994; 4 (2) :249-265.
3. Zhao SX. On absolute stability of control systems with several executive elements. Scientia Sinia (Series A) 1988; 31 (4) :395-405.
4. Wu M, He Y, Liu G, She J. On absolute stability of Lur'e control systems with multiple non-linearities. European Journal of Control 2005; 11 (1) :19-28.
5. Yang C, Zhang Q, Zhou L. Lur'e Lyapunov functions and absolute stability criteria for Lur'e systems with multiple nonlinearities. International Journal of Robust and Nonlinear Control 2007; 17 (9) :829-841.
6. Silva MS, De Lima TP. Looking for nonnegative solutions of a Leontief dynamic model. Linear Algebra and its Applications 2003; 364 (1) :281-316.
7. Campbell SL. Singular Systems of Differential Equations. Pitman: London, 1980.
8. Muller PC. Linear mechanical descriptor systems: identification, analysis and design. Preprints oflFAC. Conference on Control of Industrial Systems, Belfort, France, 1997; 501-506.
9. Cobb D. Controllability, observability and duality in singular systems. IEEE Transactions on Automatic Control 1984; 29 (12) : 1076-1082.
10. Bender DJ, Laub AJ. The linear-quadratic optimal regulator for descriptor systems. IEEE Transactions on Automatic Control 1987; 32 (8) :672-688.
11. Ishihara JY, Terra MH. On the Lyapunov theorem for singular systems. IEEE Transactions on Automatic Control 2002; 47 (11) : 1926-1930.
12. Lee L, Chen JL. Strictly positive real lemma and absolute stability for discrete-time descriptor systems. IEEE Transactions on Circuits and Systems I 2003; 50 (6) :788-794.
13. Yang C, Zhang Q, Lin Y, Zhou L. Positive realness and absolute stability problem of descriptor systems. IEEE Transactions on Circuits and Systems I: Regular Paper 2007; 54 (5) :1142-1149.
14. Yang C, Zhang Q, Zhou L. Generalised absolute stability analysis and synthesis for Lur'e-type descriptor systems. IET Control Theory and Applications 2007; l (3) :617-623.
15. Yang C, Zhang Q, Zhou L. Strongly absolute stability problem of descriptor systems. Informatica 2007; 18 (2) :305-320.
16. Yang C, Zhang Q, Zhou L. Strongly absolute stability problem of descriptor systems: circle criterion. Journal of the Franklin Institute 2008; 345 (5) :437-451.
17. Yang C, Zhang Q, Zhou L. Strongly absolute stability of Lur'e type differential-algebraic systems. Journal of Mathematical Analysis and Applications 2007; 336 (1) :188-204.
18. Yang C, Zhang Q, Zhou L. Strongly absolute stability of Lur'e type descriptor systems. Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis 2007; 14 (3) :345-361.
19. Khalil HK. Nonlinear Systems (3rd edn). Prentice-Hall: Englewood Cliffs, NJ, 1996.
20. Dai L. Singular Control Systems. Springer: Berlin, Germany, 1989.
21. Lewis EL. A survey of linear singular systems. Circuits, Systems and Signal Processing 1986; 5 (1) :3-36.
22. Brenan KE, Campbell SL, Petzold LR. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM: Philadelphia, 1996.
23. Wang H, Yung C, Chang F. H ∞ control for nonlinear descriptor systems. IEEE Transactions on Automatic Control 2002; 47 (11) :1919-1925.
24. Boyd S, Ghaoui LE. Linear Matrix Inequalities in System and Control Theory. SIAM: Philadelphia, PA, 1994.
25. Masubuchi I, Kamitane Y, Ohara A, Suda N. H ∞ control for descriptor systems: a matrix inequalities approach. Automatica 1997; 33 (4) :669-673.
26. Vladimir BB. Partial stability of motion of semi-state systems. International Journal of Control 1986; 44 (5) : 1383-1394.