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Original Articles

On an estimate of the decay rate for stable linear delay systems

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Pages 95-97 | Received 21 Dec 1981, Published online: 27 Mar 2007

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Daniel Melchor-Aguilar & Silviu-Iulian Niculescu. (2009) Computing non-fragile PI controllers for delay models of TCP/AQM networks. International Journal of Control 82:12, pages 2249-2259.
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Rong‐Jyue Wang & Wen‐June Wang. (1994) New asymptotic stability criteria for the linear time‐delay systems. Journal of the Chinese Institute of Engineers 17:5, pages 721-727.
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Te‐Jen Su & Pin‐Lin Liu. (1993) Robust stability analysis for linear uncertain time‐delay systems with delay‐dependence. Journal of the Chinese Institute of Engineers 16:4, pages 571-576.
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Juing‐Shian Chiou, Wen‐June Wang & Yn‐Shyang Jeng. (1993) Stability and robustness of time‐delay systems. Journal of the Chinese Institute of Engineers 16:4, pages 565-569.
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TE-JEN SU & PIN-LIN LIU. (1993) Robust stability for linear uncertain time-delay systems with delay-dependence. International Journal of Systems Science 24:6, pages 1067-1080.
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E. TISSIR & A. HMAMED. (1992) Further results on the stabilization of time delay systems containing saturating actuators. International Journal of Systems Science 23:4, pages 615-622.
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Te‐Jen Su & Pin‐Lin Liu. (1991) A dynamic controller for linear uncertain time‐delay systems. Journal of the Chinese Institute of Engineers 14:6, pages 639-643.
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TAKEHIRO MORI. (1986) Further comments on ‘Comments on “On an estimate of the decay rate for stable linear delay systems”’. International Journal of Control 43:5, pages 1613-1614.
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A. HMAMED. (1986) On the stability of time-delay systems: new results. International Journal of Control 43:1, pages 321-324.
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He Huang & Gang Feng. (2009) On estimating the exponential decay rate for linear systems with interval time-varying delay. On estimating the exponential decay rate for linear systems with interval time-varying delay.
Zhan Shu, James Lam & Shengyuan Xu. (2009) Improved exponential estimates for neutral systems. Asian Journal of Control 11:3, pages 261-270.
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S. Xu, J. Lam & M. Zhong. (2006) New Exponential Estimates for Time-Delay Systems. IEEE Transactions on Automatic Control 51:9, pages 1501-1505.
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Bin Liu & Xinzhi Liu. (2006) Robust Global Exponential Stability of Linear Impulsive Systems with Time-Varying Delay and Uncertainty. Rocky Mountain Journal of Mathematics 36:2.
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Vladimir Kharitonov, Joaquín Collado & Sabine Mondié. (2005) Exponential estimates for neutral time delay systems with multiple delays. International Journal of Robust and Nonlinear Control 16:2, pages 71-84.
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Ting-Li Chien, Chung-Cheng Chen & Ching-Yu Hsu. (2005) Tracking control of nonlinear automobile idle-speed time-delay system via differential geometry approach. Journal of the Franklin Institute 342:7, pages 760-775.
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V. Kharitonov, S. Mondie & J. Collado. (2005) Exponential estimates for neutral time-delay systems: an LMI approach. IEEE Transactions on Automatic Control 50:5, pages 666-670.
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S. Mondie & V.L. Kharitonov. (2005) Exponential estimates for retarded time-delay systems: an LMI approach. IEEE Transactions on Automatic Control 50:2, pages 268-273.
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V. Kharitonov, S. Mondie & J. Collado. (2004) Exponential estimates for neutral time delay systems: an LMI approach. Exponential estimates for neutral time delay systems: an LMI approach.
D.Q Cao, Ping He & Keyue Zhang. (2003) Exponential stability criteria of uncertain systems with multiple time delays. Journal of Mathematical Analysis and Applications 283:2, pages 362-374.
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S. Tarbouriech, G. Garcia & J.M. Gomes da SilvaJr.Jr.. (2002) Robust stability of uncertain polytopic linear time-delay systems with saturating inputs: an LMI approach. Computers & Electrical Engineering 28:3, pages 157-169.
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Jigen Peng, Hong Qiao & Zong-ben Xu. (2002) A new approach to stability of neural networks with time-varying delays. Neural Networks 15:1, pages 95-103.
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Yi Guo, Weibiao Zhou & Peter L. Lee. (2002) H∞ control for a class of structured time-delay systems. Systems & Control Letters 45:1, pages 35-47.
Crossref
S. Tarbouriech, G. Garcia & I. Queinnec. (2001) stabilization of linear time-delay systems with anti-stable eigenvalues under amplitude and rate saturation. IFAC Proceedings Volumes 34:23, pages 71-76.
Crossref
Zhi-Hong Guan, C.W. Chan, A.Y.T. Leung & Guanrong Chen. (2001) Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48:8, pages 1011-1019.
Crossref
S. Tarbouriech & J.M. Gomes da Silva. (2000) Synthesis of controllers for continuous-time delay systems with saturating controls via LMIs. IEEE Transactions on Automatic Control 45:1, pages 105-111.
Crossref
Yen-Hung Chen & Shu-Cherng Fang. (2000) Neurocomputing with time delay analysis for solving convex quadratic programming problems. IEEE Transactions on Neural Networks 11:1, pages 230-240.
Crossref
C.F. Alastruey, J.R.González de Mendívil & M. De la Sen. (1999) Criteria for stability in approximate delay systems. Computers & Mathematics with Applications 38:7-8, pages 199-206.
Crossref
Y. -H. Chang. (1999) Robust regional stability analysis of continuous time-delay systems. IEE Proceedings - Control Theory and Applications 146:4, pages 311-317.
Crossref
Chunhai Hou & Jixin Qian. (1999) Remarks on quantitative analysis for a family of scalar delay differential inequalities. IEEE Transactions on Automatic Control 44:2, pages 334-336.
Crossref
Chunhai Hou & Jixin Qian. (1998) On an estimate of the decay rate for applications of Razumikhin-type theorems. IEEE Transactions on Automatic Control 43:7, pages 958-960.
Crossref
S.-I. Niculescu. (1998) H/sub ∞/ memoryless control with an α-stability constraint for time-delay systems: an LMI approach. IEEE Transactions on Automatic Control 43:5, pages 739-743.
Crossref
Yeong-Jeu Sun & Jer-Guang Hsieh. (1998) On α-stability criteria of nonlinear systems with multiple time delays. Journal of the Franklin Institute 335:4, pages 695-705.
Crossref
Wen-June Wang & Rong-Jyue Wang. (1998) Robust stability for noncommensurate time-delay systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 45:4, pages 507-511.
Crossref
Bugong Xu. (1998) N&S conditions of exponential stability for retarded dynamic systems and some applications. N&S conditions of exponential stability for retarded dynamic systems and some applications.
James Louisell. 1998. Stability and Control of Time-delay Systems. Stability and Control of Time-delay Systems 140 157 .
Silviu-Iulian Niculescu, Erik I. Verriest, Luc Dugard & Jean-Michel Dion. 1998. Stability and Control of Time-delay Systems. Stability and Control of Time-delay Systems 1 71 .
E. Tissir & A. Hmamed. (1996) Further results on stability of xdot(t) = Ax(t) + Bx(t−τ). Automatica 32:12, pages 1723-1726.
Crossref
Rong-Jyue Wang & Wen-June Wang. (1996) α-Stability analysis of perturbed systems with multiple noncommensurate time delays. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 43:4, pages 349-352.
Crossref
Yeong-Hwa Chang & G.L. Wise. (1996) Stability analysis for continuous time delay systems with specified regions. Stability analysis for continuous time delay systems with specified regions.
Yeong-Jeu Sun & Jer-Guang Hsieh. (1995) A note on the stability of uncertain time-lag systems. Journal of the Franklin Institute 332:6, pages 773-782.
Crossref
Tsung-Lieh Hsien & Chien-Hua Lee. (1995) Exponential stability of discrete time uncertain systems with time-varying delay. Journal of the Franklin Institute 332:4, pages 479-489.
Crossref
C.F. Alastruey, M. De La Sen & J.R.González De Mendívil. (1995) The stabilizability of integro-differential systems with two distributed delays. Mathematical and Computer Modelling 21:8, pages 85-94.
Crossref
Jie Chen, Demin Xu & B. Shafai. (1995) On sufficient conditions for stability independent of delay. IEEE Transactions on Automatic Control 40:9, pages 1675-1680.
Crossref
Jie Chen & H.A. Latchman. (1995) Frequency sweeping tests for stability independent of delay. IEEE Transactions on Automatic Control 40:9, pages 1640-1645.
Crossref
E. Tissir & A. Hmamed. (1994) Stability tests of interval time delay systems. Systems & Control Letters 23:4, pages 263-270.
Crossref
Jie Chen. (1994) On computing the maximal delay intervals for stability of linear delay systems. On computing the maximal delay intervals for stability of linear delay systems.
Jie Chen, Demin Xu & B. Shafai. (1994) On sufficient conditions for stability independent of delay. On sufficient conditions for stability independent of delay.
J. Chen & H.A. Latchman. (1994) Asymptotic stability independent of delays: simple necessary and sufficient conditions. Asymptotic stability independent of delays: simple necessary and sufficient conditions.
B. Lehman & K. Shujaee. (1994) Delay independent stability conditions and decay estimates for time-varying functional differential equations. IEEE Transactions on Automatic Control 39:8, pages 1673-1676.
Crossref
Shuenn-Shyang Wang. (1992) Further results on stability of. Systems & Control Letters 19:2, pages 165-168.
Crossref
J.-H. Su, I.-K. Fong & C.-L. Tseng. (1992) Stability analysis of systems with commensurate time delays. Stability analysis of systems with commensurate time delays.
W.-J. Wang, J.-S. Chiou & Y.-S. Jeng. (1992) A new robust stability criterion for interval time-delay systems. A new robust stability criterion for interval time-delay systems.
T.-J. Su & C.-G. Huang. (1992) Robust stability of delay dependence for linear uncertain systems. IEEE Transactions on Automatic Control 37:10, pages 1656-1659.
Crossref
T. Mori & H. Kokame. (1989) Stability of x(t)=Ax(t)+Bx(t- tau ). IEEE Transactions on Automatic Control 34:4, pages 460-462.
Crossref

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