Optimal partitioning method for stability analysis of continuous/discrete delay systems

International Journal of Robust and Nonlinear Control

Volumn 25, Issue 4, 2015, Pages 559-574

  Feng, Zhiguang ^a   Lam, James ^b   Yang, Guang Hong ^c,d  

^a BOHAI UNIVERSITY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c NORTHEASTERN UNIVERSITY   (China)

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

Author keywords

Continuous time systems; Delay partitioning; Discrete time systems; Time varying delay

Indexed keywords

DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; GENETIC ALGORITHMS; LINEAR MATRIX INEQUALITIES; SYSTEM STABILITY; TIME DELAY; TIME VARYING CONTROL SYSTEMS;

DELAY PARTITIONING; DISCRETE - TIME SYSTEMS; INTERVAL TIME-VARYING DELAYS; NEW LYAPUNOV FUNCTIONALS; OPTIMAL PARTITIONING; STABILITY ANALYSIS; STABILITY CONDITION; TIME VARYING- DELAYS;

CONTINUOUS TIME SYSTEMS;

EID: 84921067545     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.3106     Document Type: Article

References (35)

1. He Y, Wang QG, Lin C, Wu M. Delay-range-dependent stability for systems with time-varying delay. Automatica 2007; 43(2):371-376.
2. Shao H. New delay-dependent criteria for systems with interval delay. Automatica 2009; 45:744-749.
3. Park PG, Ko JW, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica 2011; 47:235-238.
4. Sun J, Liu GP, Chen J, Rees D. Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 2010; 46(2):466-470.
5. Fridman E, Shaked U, Liu K. New conditions for delay-derivative-dependent stability. Automatica 2009; 45(11):2723-2727.
6. Mou S, Gao H, Chen T. New delay-range-dependent stability condition for linear system. Proceedings of 7th World Congress on Intelligent Control and Automation, Chongqing, China, 2008; 313-316.
7. Zhu X, Yang G. Jensen integral inequality approach to stability analysis of continuous-time systems with time-varying delay. IET Control Theory and Applications 2008; 2(6):524-534.
8. Du B, Lam J, Shu Z, Wang Z. A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components. IET Control Theory and Applications 2009; 3:383-390.
9. Zhang XM, Han QL. New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks. IEEE Transactions on Neural Networks 2009; 20(3):533-539.
10. Zhang H, Liu Z. Stability analysis for linear delayed systems via an optimally dividing delay interval approach. Automatica 2011; 47:2126-2129.
11. Zhu X, Yang G. New results of stability analysis for systems with time-varying delay. International Journal of Robust and Nonlinear Control 2010; 20:596-606.
12. Shao H. Improved delay-dependent stability criteria for systems with a delay varying in a range. Automatica 2008; 44:3215-3218.
13. Hu S, Yan WY. Stability robustness of networked control systems with respect to packet loss. Automatica 2007; 43(7):1243-1248.
14. Xiong J, Lam J. Stabilization of linear systems over networks with bounded packet loss. Automatica 2007; 43(1):80-87.
15. Gao H, Lam J, Wang C, Wang Y. Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proceedings - Control Theory and Applications 2004; 151:691-698.
16. Li Q, Wang Y, Zhu H, Hu Y. Delay-partition-dependent robust stability criteria for uncertain discrete-time systems with an interval time-varying state delay. Advances in Computer, Communication, Control and Automation 2011:557-564.
17. Ma S, Boukas EK, Chinniah Y. Stability and stabilization of discrete-time singular Markov jump systems with time-varying delay. International Journal of Robust and Nonlinear Control 2010; 20:531-543.
18. Xu S, Lam J, Zou Y. Improved conditions for delay-dependent robust stability and stabilization of uncertain discrete time-delay systems. Asian Journal of Control 2005; 7(3):344-348.
19. Zhu X, Yang G. Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay. Proceedings of American Control Conference, Washington, DC, USA, 2008; 1644-1649.
20. Gao H, Chen T. New results on stability of discrete-time systems with time-varying state delay. IEEE Transactions on Automatic Control 2007; 52:328-334.
21. Zhang B, Xu S, Zou Y. Improved stability criterion and its applications in delayed controller design for discrete-time systems. Automatica 2008; 44:2963-2967.
22. Shao H, Han QL. New stability criteria for linear discrete-time systems with interval-like time-varying delays. IEEE Transactions on Automatic Control 2011; 56:619-625.
23. Meng X, Lam J, Gao H, Du B. A delay-partitioning approach to stability analysis of discrete-time systems. Automatica 2010; 46:610-614.
24. Gu K, Kharitonov V, Chen J. Stability of Time-Delay Systems. Birkhauser: Boston, MA, USA, 2003.
25. Jiang X, Han QL, Yu X. Stability criteria for linear discrete-time systems with interval-like time-varying delay. Proceedings of American Control Conference, Portland, OR, USA, 2005; 2817-2822.
26. Yue D, Tian E, Zhang Y. A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay. International Journal of Robust and Nonlinear Control 2009; 19:1493-1518.
27. Arfiadi Y, Hadi MNS. Optimal direct (static) output feedback controller using real coded genetic algorithms. Computers & Structures 2001; 79(17):1625-1634.
28. 2 approximation of multiple input-output delay systems using genetic algorithm. ISA Transactions 2007; 46(2):211-221.
29. ∞ vehicle suspension control using genetic algorithm. Engineering Applications of Artificial Intelligence 2003; 16(7):667-680.
30. ∞ control for buildings with time delay in control via linear matrix inequalities and genetic algorithms. Engineering Structures 2008; 30(1):81-92.
31. ∞ controllers for time-delay systems using genetic algorithms. Control and Intelligent Systems 2007; 35(4):395-400.
32. Lam J, Tam HK. Robust output feedback pole assignment using genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2000; 214(5):327-334.
33. Haupt RL, Haupt SE, Wiley J. Practical Genetic Algorithms. Wiley: New York, USA, 2004.
34. Zhu X, Yang G. A delay decomposition approach to stability analysis of discrete-time systems with time-varying delay. Proceedings of American Control Conference, St. Louis, MO, USA, 2009; 5465-5468.
35. Peng C. Improved delay-dependent stabilisation criteria for discrete systems with a new finite sum inequality. IEE Proceedings - Control Theory and Applications 2012; 6:448-453.