This note is concerned with the problem of delay-dependent stability for discrete-time systems with time-varying delay. Two novel delay-dependent stability conditions are established by bounding the forward difference of the Lyapunov functional based on the reciprocally convex approach and a scale inequality, respectively. These criteria improve the existing ones with smaller computation burden and less conservatism, which is verified by both theoretical proof and a numerical example.
Inspec keywords: discrete time systems; convex programming; time-varying systems; delay systems; stability; Lyapunov methods
Other keywords:
Subjects: Stability in control theory; Other numerical methods; Optimisation techniques; Discrete control systems; Distributed parameter control systems; Time-varying control systems
References
-
-
1)
- E. Fridman , U. Shaked . Stability and guaranteed cost control of uncertain discrete delay systems. Int. J. Control , 235 - 246
-
2)
- Briat, C.: `Robust control and observation of LPV time-delay systems', 2008, PhD, Grenoble INP, France.
-
3)
- Y. He , M. Wu , G.P. Liu , J.H. She . Output feedback stabilization for a discrete time system with a time-varying delay. IEEE Trans. Autom. Control , 10 , 2372 - 2377
-
4)
- B.Y. Zhang , S.Y. Xu , Y. Zhou . Improved stability criterion and its applications in delayed controller design for discrete time systems. Automatica , 2963 - 2967
-
5)
- Q.-L. Han . Improved stability criteria and controller design for linear neutral systems. Automatica , 8 , 1948 - 1952
-
6)
- Zhu, X.L., Yang, G.H.: `Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay', American Control Conf., 2008, Seattle, WA, p. 1644–1649.
-
7)
- H. Gao , J. Lam , C. Wang , Y. Wang . Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay. IEE Proc. Control Theory Appl. , 6 , 691 - 698
-
8)
- Y. Wu , Y. Wu , Y. Chen . Mean square exponential stability of uncertain stochastic neural networks with time-varying delay. Neurocomputing , 2379 - 2384
-
9)
- K. Gu , V.L. Kharitonov , J. Chen . (2003) Stability of time-delay systems.
-
10)
- H.Y. Shao , Q.-L. Han . New stability criteria for linear discrete time systems with interval-like time-varying delays. IEEE Trans. Autom. Control , 3 , 619 - 625
-
11)
- Jiang, X., Han, Q., Yu, X.: `Stability criteria for linear discrete-time systems with interval-like time-varying delay', Proc. American Control Conf. 2005, 2005, p. 2817–2822.
-
12)
- P. Park , J. Wan Ko . Stability and robust stability for systems with a time-varying delay. Automatica , 10 , 1855 - 1858
-
13)
- P. Park , J.W. Ko , C. Jeong . Reciprocally convex approach to stability of systems with time-varying delays. Automatica , 1 , 235 - 238
-
14)
- Gu, K.: `Partial solution of LMI in stability problem of time-delay systems', Proc. 38th IEEE Conf. Decision and Control., 1999, Phoenix, Arizona, p. 227–232.
-
15)
- 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 , 630 - 647
-
16)
- H. Gao , T. Chen . New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control , 2 , 328 - 334
-
1)
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