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International Journal of Control Volume 50, 1989 - Issue 5
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Original Articles

Robust stability of polynomials with multilinear parameter dependence

F. J. KRAUS Department of Automatic Control and Industrial Engineering, Swiss Federal Institute of Technology, ETH-Zentrum, Zürich, Switzerland
,
B. D. O. ANDERSON Department of Systems Engineering, Australian National University The work of this author was predominantly performed at the Swiss Federal Institute of Technology, Zürich, Canberra, ACT 2601, Australia
&
M. MANSOUR Department of Automatic Control and Industrial Engineering, Swiss Federal Institute of Technology, ETH-Zentrum, Zürich, Switzerland
Pages 1745-1762 | Received 15 Feb 1988, Published online: 16 May 2007

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Jong‐Yih Lin & Tsai‐Wan Chen. (2001) A direction method for stability robustness analysis with respect to real uncertain parameters. Journal of the Chinese Institute of Engineers 24:4, pages 509-516.
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AURELIO PIAZZI & GIOVANNI MARRO. (1996) Robust stability using interval analysis. International Journal of Systems Science 27:12, pages 1381-1390.
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Johnson Y. Robust PID control of a tuned mass damper system and its stability analysis validation by Kharitonov and Edge theorems. Australian Journal of Multi-Disciplinary Engineering 0:0, pages 1-10.
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Articles from other publishers (33)

Fatemeh Amini & Hamid Khaloozadeh. (2017) Robust stabilization of multilinear interval plants by Takagi–Sugeno fuzzy controllers. Applied Mathematical Modelling 51, pages 329-340.
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M.J. Knap, L.H. Keel & S.P. Bhattacharyya. (2011) Robust Hurwitz stability via sign-definite decomposition. Linear Algebra and its Applications 434:7, pages 1663-1676.
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Ilhan Tuzcu & Mehdi Ahmadian. (2002) Delay-independent Stability of Uncertain Control Systems. Journal of Vibration and Acoustics 124:2, pages 277-283.
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K. Tsumura & M. Kitamura. (2002) Structural analysis of robust control systems. IEEE Transactions on Automatic Control 47:1, pages 125-132.
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Wen-Hua Chen & Donald J. Ballance. (1999) Plant Template Generation for Uncertain Plants in Quantitative Feedback Theory. Journal of Dynamic Systems, Measurement, and Control 121:3, pages 358-364.
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Nainn-Ping Ke. (1999) A New Method to Compute Complex Stability Margin. IFAC Proceedings Volumes 32:2, pages 3237-3242.
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Nainn-Ping Ke. (1998) Value set versus Horowitz template in robust stability analysis. Value set versus Horowitz template in robust stability analysis.
Chyi Hwang & Jyh-Jia Chen. (1998) Plotting robust root loci for linear systems with multilinearly parametric uncertainties. Plotting robust root loci for linear systems with multilinearly parametric uncertainties.
Nainn-Ping Ke. (1998) An algorithm of symbolic computation for stability margin. An algorithm of symbolic computation for stability margin.
Takeshi Kawamura & Masasuke Shima. (1997) Robust stability of characteristic polynomials with monotonicity. Nonlinear Analysis: Theory, Methods & Applications 30:8, pages 5109-5119.
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L.R. Pujara & B.B. Srinivas. (1997) On the robust stability of characteristic polynomials with multilinear coefficients. Nonlinear Analysis: Theory, Methods & Applications 30:5, pages 3093-3100.
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Wolfgang Sienel. (1996) On Stability Profiles. IFAC Proceedings Volumes 29:1, pages 3410-3415.
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G. Chen & T. Sugie. (1996) New upper bound of the real μ based on the parameter dependent multiplier. New upper bound of the real μ based on the parameter dependent multiplier.
B.T. Polyak & J. Kogan. (1995) Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure. IEEE Transactions on Automatic Control 40:7, pages 1255-1260.
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Weining Chen & I.R. Petersen. (1995) A class of multilinear uncertain polynomials to which the edge theorem is applicable. IEEE Transactions on Automatic Control 40:12, pages 2103-2107.
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Minyue Fu, S. Dasgupta & V. Blondel. (1995) Robust stability under a class of nonlinear parametric perturbations. IEEE Transactions on Automatic Control 40:2, pages 213-223.
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B.D.O. Anderson, F. Kraus, M. Mansour & S. Dasgupta. (1995) Easily testable sufficient conditions for the robust stability of systems with multilinear parameter dependence. Automatica 31:1, pages 25-40.
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. 1995. Robust Stability and Convexity. Robust Stability and Convexity 153 156 .
Christopher L. Demarco & Gregory E. Coxson. 1995. Systems and Control Theory For Power Systems. Systems and Control Theory For Power Systems 117 136 .
Weining Chen & I.R. Petersen. (1994) A class of multilinear uncertain polynomials to which the Edge theorem is applicable. A class of multilinear uncertain polynomials to which the Edge theorem is applicable.
G. Chockalingam & S. Dasgupta. (1994) Strong stabilizability of systems with multiaffine uncertainties and numerator denominator coupling. IEEE Transactions on Automatic Control 39:9, pages 1955-1958.
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A.M. Holohan & M.G. Safonov. (1993) Some counterexamples in robust stability theory. Systems & Control Letters 21:2, pages 95-102.
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Nam-Kiu Tsing & AndréL. Tits. (1993) When is the multiaffine image of a cube a convex polygon?. Systems & Control Letters 20:6, pages 439-445.
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S.J. Xu, M. Darouach & J. Schaefers. (1993) Expansion of det(A+B) and robustness analysis of uncertain state space systems. IEEE Transactions on Automatic Control 38:11, pages 1671-1675.
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P. Dorato, R. Tempo & G. Muscato. (1993) Bibliography on robust control. Automatica 29:1, pages 201-213.
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B.D.O. Anderson, F.J. Kraus, M. Mansour & S. Dasgupta. (1992) Sufficient Conditions for the Robust Stability of Systems with Multiaffine Parameter Dependence. IFAC Proceedings Volumes 25:21, pages 168-171.
Crossref
C.-H. CHUANG, C.-T. KAU & JER-NAN JUANG. (1992) Determination of robust stability margin for second-order systems. Determination of robust stability margin for second-order systems.
L.R. Pujara & S. Kim. (1992) An application of the pseudo boundary of an unstable polytope of polynomials. An application of the pseudo boundary of an unstable polytope of polynomials.
B.D.O. Anderson, F.J. Kraus, M. Mansour & S. Dasgupta. 1992. System Structure and Control 1992. System Structure and Control 1992 168 171 .
B. D. O. Anderson, F. J. Kraus, M. Mansour & S. Dasgupta. 1992. Robustness of Dynamic Systems with Parameter Uncertainties. Robustness of Dynamic Systems with Parameter Uncertainties 81 92 .
Nam-Kiu Tsing & André L. Tits. 1992. Robustness of Dynamic Systems with Parameter Uncertainties. Robustness of Dynamic Systems with Parameter Uncertainties 105 110 .
B. T. Polyak. 1992. Robustness of Dynamic Systems with Parameter Uncertainties. Robustness of Dynamic Systems with Parameter Uncertainties 93 104 .
M. Mansour & F.J. Kraus. (1989) Robust stability of systems with nonlinear parameter dependence. Robust stability of systems with nonlinear parameter dependence.

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