Directional stability radius: a stability analysis tool for uncertain polynomial systems

Kawabata, Keishi; Mori, Takahide; Kuroe, Yasuaki

doi:10.1109/tac.2003.812785

Cited by 11 publications

(5 citation statements)

References 5 publications

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“…In this section, being different from previous sections, the authors describe an approach to perform stability analysis of a polytopic polynomial using a directional stability radius [8][9][10] to guarantee set-term stability. The definition of a polytopic polynomial here discussed involves operators including the delta operator ε in Eq.…”

Section: A Methods Using a Directional Stability Radiusmentioning

confidence: 99%

“…The first is a method using a matrix eigenvalue, and the second is a method using the concept of value sets. Moreover, separate from these methods derived is an extension of a method [8][9][10] that uses a directional stability radius which was proposed as a method for stability analysis for interval polynomials and diamond polynomials. This method can be adapted to polytopic polynomials.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis methods for delta operator polytopic polynomials

Matsuda

Kawabata

Mori

2007

Electrical Engineering Japan

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SUMMARYStability analysis of a linear uncertain polynomial system in parameter space is one of the central themes of recent control theory. It often requires an enormous number of stability checks with conventional stability test methods. A delta operator polytopic polynomial, a convex combination of some delta operator vertex polynomials, is one of such cases. In this paper, robust stability is addressed for polytopic delta operator polynomials and several necessary and sufficient stability conditions are derived. The delta operator, an operator used to express discrete time systems, is known to have significant features: numerical advantage in implementation and ability to smoothly connect the z-operator with the Laplace operator. Based on this last feature and on the celebrated Edge theorem, we first derive three kinds of exact stability conditions for the uncertain delta operator polynomials. We then extend the directional stability radius method, which was developed for diamond polynomials, so that it can also be applied to polytopic polynomials. This extension gives rise to the fourth stability test. Furthermore, it is shown from the result of the numerical experiments with these stability analysis methods that one of these four methods, which uses eigenvalues of matrices, turns out to be most efficient for stability analysis of the polytope.

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Section: A Methods Using a Directional Stability Radiusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability analysis methods for delta operator polytopic polynomials

Matsuda

Kawabata

Mori

2007

Electrical Engineering Japan

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“…A method using LMI formulation is shown in [19]. The stability radius [20], [21] and the directional stability radius [22] are tools to derive the stability ranges of uncertain systems.…”

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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“…It is often required to determine range of a parameter of a system such that the system remains stable. Stability radius [9,10], directional stability radius [11], a method given in [12] based on the result by Bialas [6], methods in [13,14,15,16,17,18] based on Lyapunov stability theory, and methods in [19,20,21] using the guardian maps meet such a demand.…”

Section: Introductionmentioning

confidence: 99%