Stability analysis and output-feedback stabilisation of discrete-time systems with an interval time-varying state delay
Stability analysis and output-feedback stabilisation of discrete-time systems with an interval time-varying state delay
- Author(s): K.F. Chen and IK. Fong
- DOI: 10.1049/iet-cta.2009.0100
For access to this article, please select a purchase option:
Buy article PDF
Buy Knowledge Pack
IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.
Thank you
Your recommendation has been sent to your librarian.
- Author(s): K.F. Chen 1 and IK. Fong 1
-
-
View affiliations
-
Affiliations:
1: Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan
-
Affiliations:
1: Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan
- Source:
Volume 4, Issue 4,
April 2010,
p.
563 – 572
DOI: 10.1049/iet-cta.2009.0100 , Print ISSN 1751-8644, Online ISSN 1751-8652
This study focuses on the stability of discrete-time systems with a time-varying state delay and uncertainties in system matrices. New linear matrix inequality conditions are derived for determining bounds of the delay size to ensure the asymptotic stability. There is no need to assume that the system is stable when the delay vanishes. Conservativeness of the conditions is reduced as much as possible by introducing the free-weighting matrices in a novel way, and using the least inequality in the derivation process. Then a new static output-feedback stabilisation method is proposed with the gain matrix as a direct design variable. Compared with the existing results, the proposed methods indeed give larger delay bounds for many cases.
Inspec keywords: delays; linear matrix inequalities; asymptotic stability; control system synthesis; discrete time systems; time-varying systems; feedback
Other keywords:
Subjects: Stability in control theory; Control system analysis and synthesis methods; Time-varying control systems; Distributed parameter control systems; Discrete control systems; Algebra
References
-
-
1)
- E.K. Boukas . Discrete-time systems with time-varying time delay: stability and stabilizability. Math. Probl. Engng. , 1 , 1 - 10
-
2)
- X.G. Liu , R.R. Martin , M. Wu , M.L. Tang . Delay-dependent robust stabilization of discrete-time systems with time-varying delay. IEE Proc. Control Theory Appl. , 6 , 689 - 702
-
3)
- K.F. Chen , IK. Fong . Stability of discrete-time uncertain systems with a time-varying state delay. Proc. IMechE, Part I: J. Syst. Control Engng. , 6 , 493 - 500
-
4)
- H. Gao , J. Lam , C. Wang , Y. Wang . Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proc. Control Theory Appl. , 6 , 691 - 698
-
5)
- E. Fridman , U. Shaked . Stability and guaranteed cost control of uncertain discrete delay systems. Int. J. Control , 4 , 235 - 246
-
6)
- S. Boyd , L. El Ghaoui , E. Feron , V. Balakrishnan . (1994) Linear matrix inequalities in systems and control theory.
-
7)
- Knospe, C.R., Roozbehani, M.: `Stability of linear systems with interval time-delay', Proc. American Control Conf., June 2003, Denver, CO, p. 1458–1463.
-
8)
- M.S. Mahmoud . (2000) Robust control and filtering for time-delay systems.
-
9)
- K. Gu , V.L. Kharitonov , J. Chen . (2003) Stability of time-delay systems.
-
10)
- Y. Xia , G.P. Liu , P. Shi , D. Rees , E.J.C. Thomas . New stability and stabilization conditions for systems with time-delay. Int. J. Syst. Sci. , 1 , 17 - 24
-
11)
- Zhu, X.L., Yang, G.H.: `Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay', Proc. American Control Conf., June 2008, Seattle, WA, p. 1644–1649.
-
12)
- Q.X. Chen , L. Yu , W.A. Zhang . Delay-dependent output feedback guaranteed cost control for uncertain discrete-time systems with multiple time-varying delays. IEE Proc. Control Theory Appl. , 1 , 97 - 103
-
13)
- L. El Ghaoui , F. Oustery , M. AitRami . A cone complementarity linearization algorithm for static output feedback and related problems. IEEE Trans. Autom. Control , 8 , 1171 - 1176
-
14)
- J. Zhang , C.R. Knopse , P. Tsiotras . Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions. IEEE Trans. Autom. Control , 3 , 482 - 486
-
15)
- D. Yue , Q.L. Han , J. Lam . Network-based robust H∞ control of systems with uncertainty. Automatica , 6 , 999 - 1007
-
16)
- Abdallah, C.T., Chiasson, J.: `Stability of communications networks in the presence of delays', Proc. Third IFAC Workshop on Time Delay Systems, December 2001, Santa Fe, NM, p. 8–10.
-
17)
- Y. Lee , J. Lee , S. Park . PID controller tuning for integrating and unstable processes with time delay. Chem. Eng. Sci. , 17 , 3481 - 3493
-
18)
- X. Li , C.E. de Souza . Delay-dependent robust stability and stabilization of uncertain linear delay system: a linear matrix inequality approach. IEEE Trans. Autom. Control , 8 , 1144 - 1148
-
19)
- X.M. Zhang , Q.L. Han . A new finite sum inequality approach to delay-dependent H∞ control of discrete-time systems with time-varying delay. Int. J. Robust Nonlinear Control. , 6 , 630 - 647
-
20)
- J. Hale , Verduyn , S.M. Lunel . (1993) Introduction to functional differential equations.
-
21)
- S. Ma , Z. Cheng , C. Zhang . Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays. IEE Proc. Control Theory Appl. , 4 , 1086 - 1095
-
22)
- Jiang, X., Han, Q.L., Yu, X.: `Stability criteria for linear discrete-time systems with interval-like time-varying delay', Proc. American Control Conf., June 2005, Portland, OR, p. 2817–2822.
-
23)
- Y. He , M. Wu , G. Liu , J. She . Output feedback stabilization for a discrete-time system with a time-varying delay. IEEE Trans. Autom. Control , 10 , 2372 - 2377
-
24)
- M. Shamsuzzoha , M. Lee . IMC-PID controller design for improved disturbance rejection of time-delayed processes. Ind. Eng. Chem. Res. , 7 , 2077 - 2091
-
25)
- Wang, C., Wang, Y.: `Design networked control systems via time-varying delay compensation approach', Proc. Fifth World Congress Intelligent Control Automation, June 2004, Hangzhou, P.R. China, p. 1371–1375.
-
26)
- Chiasson, J., Abdallah, C.T.: `Robust stability of time delay systems: theory', Proc. Third IFAC Workshop on Time Delay Systems, December 2001, Santa Fe, NM, p. 125–130.
-
27)
- Zhang, J., Wang, N., Wang, S.: `A developed method of tuning PID controllers with fuzzy rules for integrating processes', Proc. American Control Conf., June 2004, Boston, MA, p. 1109–1114.
-
28)
- P. Gahinet , A. Nemirovski , A.J. Laub , M. Chilali . (1995) LMI control toolbox for use with MATLAB.
-
29)
- H. Gao , T. Chen . New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control , 2 , 328 - 334
-
30)
- Y. Wang , Y. Zuo , L. Huang , Z. Wang . A new delay-dependent H∞ control criterion for a class of discrete-time systems with time-varying state delays and input delays. Proc. IMechE, Part I: J. Syst. Control Eng. , 8 , 863 - 874
-
31)
- M. Chidambaram , R. Padma Sree . A simple method of tuning PID controllers for integrator/dead-time processes. Comput. Chem. Eng. , 2 , 211 - 215
-
32)
- D. Yue , Q.L. Han , C. Peng . State feedback controller design of networked control systems. IEEE Trans. Circuits Syst., II Express Briefs , 11 , 640 - 644
-
33)
- H.Q. Zhou , Q.G. Wang , L.S. Shieh . PID control of unstable processes with time delay: a comparative study. Ind. Eng. Chem. Res. , 2 , 145 - 163
-
1)
Related content
