Stability Feeler: a tool for parametric robust stability analysis and its applications

Matsuda, Tadamitsu; Mori, T.

doi:10.1049/iet-cta.2008.0462

Cited by 18 publications

(27 citation statements)

References 10 publications

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“…The stability feeler [31] is a tool to derive complete intervals ofδ i such that the following characteristic polynomial family…”

Section: Stability Feelermentioning

confidence: 99%

“…On the other hand, many results on stability analysis of uncertain polynomials by using a class of approaches inspired by Kharitonov's work [21] have also been given in [22]- [31]. The edge theorem is given in [25].…”

Section: Introductionmentioning

confidence: 99%

“…Largest hypersphere containing only stable polynomials in the coefficient space is derived by the method in [28]. The directional stability radius and the stability feeler, which are tools for robust stability analysis for systems with parametric uncertainties, are proposed in [29] and [31], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…In order to bridge the gap between these approaches, Matsuda et al [34]- [37] have given some methods to compute an upper bound and a lower bound of the real μ using the sta-bility feeler [31], a tool for robust stability analysis of polynomials. These methods enable one to analyze Hurwitz stability of linear systems with real structured uncertainties.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust D-Stability Analysis of Linear Systems with Real Structured Uncertainties by the Stability Feeler

Matsuda

Kawanishi

Narikiyo

2014

SICE Journal of Control, Measurement, and System Integration

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: This paper gives a new method for robust D-stability analysis of linear systems with real structured uncertainties using the stability feeler. The proposed method has an improvement over past ones presented in a couple of conference papers. Past ones can be applied only to Hurwitz stability analysis. On the other hand, the proposed method can be applied to not only Hurwitz stability analysis, but also other D-stability analysis.

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“…The stability feeler [31] is a tool to derive complete intervals ofδ i such that the following characteristic polynomial family…”

Section: Stability Feelermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust D-Stability Analysis of Linear Systems with Real Structured Uncertainties by the Stability Feeler

Matsuda

Kawanishi

Narikiyo

2014

SICE Journal of Control, Measurement, and System Integration

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“…The stability feeler [23] also meets such a demand, which enables one to derive the stability ranges of a segment polynomial. The stability feeler can be applied to many types of stability analysis if the stability region in the complex plane is connected.…”

Section: Introductionmentioning

confidence: 99%

Derivation of Robust Stability Ranges for Disconnected Region with Multiple Parameters

Matsuda

2017

SICE Journal of Control, Measurement, and System Integration

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: The aim of this paper is to give an extension of the paper [T. Matsuda et al. Proc. 33rd IASTED Modelling, Identification and Control, 809-004, 2014], which gives a robust stability condition for a system with disconnected stability regions. The considered system depends on only one uncertain parameter. In this paper, an explicit algorithm to derive the stability ranges for disconnected stability regions is given. We also extend the result to the case that the system depends on multiple uncertain parameters. A numerical example shows that the proposed method can be applied to robust stability analysis of the lateral dynamics of an aircraft even if all the coefficients of the characteristic polynomial vary. The numerical example also shows that the stability ranges derived by the proposed method are larger than those by a former method.

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Steady‐state process optimization with guaranteed robust stability under parametric uncertainty

Chang

Sahinidis

2011

AIChE Journal

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Interest in chemical processes that perform well in dynamic environments has led to the development of design methodologies that account for operational aspects of processes, including flexibility, operability, and controllability. In this article, we address the problem of identifying process designs that optimize an economic objective function and are guaranteed to be stable under parametric uncertainties. The underlying mathematical problem is difficult to solve as it involves infinitely many constraints, nonconvexities and multiple local optima. We develop a methodology that embeds robust stability constraints to steady-state process optimization formulations without any a priori bifurcation analysis. We propose a successive row and column generation algorithm to solve the resulting generalized semi-infinite programming problem to global optimality. The proposed methodology allows modeling different levels of robustness, handles uncertainty regions without overestimating them, and works for both unique and multiple steady states. We apply the proposed approach to a number of steady-state optimization problems and obtain the least conservative solutions that guarantee robust stability.

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Stability Feeler: a tool for parametric robust stability analysis and its applications

Cited by 18 publications

References 10 publications

Robust D-Stability Analysis of Linear Systems with Real Structured Uncertainties by the Stability Feeler

Robust D-Stability Analysis of Linear Systems with Real Structured Uncertainties by the Stability Feeler

Derivation of Robust Stability Ranges for Disconnected Region with Multiple Parameters

Steady‐state process optimization with guaranteed robust stability under parametric uncertainty

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