Value sets of polynomial families with coefficients depending nonlinearly on perturbed parameters

Chen, Jyh‐Jia; Hwang, Chyi

doi:10.1049/ip-cta:19981718

Cited by 7 publications

(10 citation statements)

References 14 publications

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“…We call such a GPP manifold an isolated GPP manifold. For a non-isolated or connecting GPP manifold, it possesses the following connectedness property (Chen and Hwang, 1998).…”

Section: Bab)mentioning

confidence: 99%

“…Suppose that the domain D is symmetric with respect to the real axis of the complex plane C, and that its boundary above the real axis, denoted by dD + , possesses the parametric representation: (8) where (j)(qo) is a complex-valued function, e.g., 0(//o) =jqo, j=\J-1 for the Hurwitz stability domain, and 0(q o )=e i ' l o for the Schur stability domain. Then, according to the zero-exclusion principle, we know that all the members of the polynomial family p(s; E r (q°, w)) are D-stable if and only if there is a parameter vector q such that p(s;q) is D-stable and the value set p(dD + ; E r (q°, w)) does not contain the origin 0+/0.…”

Section: Formulation Of the Problemsmentioning

confidence: 99%

“…They presented an explicit characterization of the set of principal points P and showed that the image of P covers the value-set boundary df(B), i.e., df(B)af(P). Very recently, Chen and Hwang (1998) have generalized the notion of principal points such that a generalized principal point admits an analytic characterization. They also provided theorems of identifying the set of principal points P from the set of generalized principal points (GPPs) G. The set of generalized principal-points G consists of connecting and isolated one-dimensional GPP manifolds on the edges, the faces, and the interior of the box B.…”

Section: Introductionmentioning

confidence: 99%

“…It is noted that an isolated GPP manifold is closed on an open face or in the interior of B, while each connecting GPP manifold branch on a ^-dimensional face (d-face) F d emanates from and ends at the connecting GPP manifolds on (d-l)-subfaces of F d . Based on such a connectedness property, Chen and Hwang (1998) have developed a simplicial algorithm for tracing out all connecting GPP manifolds. This GPP manifold tracing algorithm has been applied to the robust stability analysis (Chen and Hwang, 1998) and //""-norm computation (Hwang et al, 1997) for linear uncertain systems with coefficients depending nonlinearly on parameters in an m-box B.…”

Section: Introductionmentioning

confidence: 99%

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Robust stability and performance analysis of feedback control for plants with uncertain parameters in an ellipsoid

Hwang

Yang

2000

Journal of the Chinese Institute of Engineers

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In this paper, we consider the problems of robust stability analysis and H -norm computation for a feedback control system in which the plant is subjected to parametric variations in an m-dimensional ellipsoid (m-ellipsoid) E. It is shown that the problems can be solved in a unified framework of constructing the image or value set f(B) of an m-box B under a differentiable complex-valued mapping f. The value set/(B) is constructed through finding the set of the generalized principal-point (GPP) manifolds G of dimension one whose image f(G) converts the value-set boundary f(B). The set G consists of connecting GPP manifolds, which have a connection with the edges of B, and isolated GPP manifolds which are closed curves on the open faces of B. The set of connecting GPP manifolds G c are traced out by a spherical algorithm such that the computed outer border of f(G c ) is ε-connected, i.e., the distance of the nearest neighbour is less than ε. This allows the isolated GPP manifolds whose images may have a substantial contribution to the value-set boundary f(B) to be almost detected and then found.

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“…We call such a GPP manifold an isolated GPP manifold. For a non-isolated or connecting GPP manifold, it possesses the following connectedness property (Chen and Hwang, 1998).…”

Section: Bab)mentioning

confidence: 99%

Section: Formulation Of the Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust stability and performance analysis of feedback control for plants with uncertain parameters in an ellipsoid

Hwang

Yang

2000

Journal of the Chinese Institute of Engineers

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“…In the following, we apply the notion of principal points [29][30][31] to characterize the boundary of the H ∞ constraint set E(k d ,γ), i.e., to characterize ∂E(k d ,γ).…”

Section: Construction Of H ∞ Constraint Domainmentioning

confidence: 99%

A New Approach to Mixed H₂/H_∞ Optimal PI/PID Controller Design

Hwang

Hsiao

2002

Ind. Eng. Chem. Res.

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This paper proposes a new approach to the problem of designing optimal proportional-integralderivative (PID) controllers that minimize an H 2 norm associated with the set-point response subjected to a constraint on the H ∞ norm of disturbance rejection. The proposed design approach consists of constructing the feasible domain in the controller gain space and searching over the domain for the optimal gain values of minimizing the H 2 -norm objective function. The construction of the feasible domain that satisfies the requirements of closed-loop stability and H ∞ -norm constraint is achieved through analytic characterization of the domain boundary with the notion of principal points associated with the value set of a differentiable mapping. The constructed feasible domain saves greatly on the computational effort requied to search for the H 2 -optimal controller gain values that satisfy both the stability and disturbance rejection requirements.

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Stability and D -stability of the family of real polynomials

Kalinina

2013

Linear Algebra and its Applications

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Value sets of polynomial families with coefficients depending nonlinearly on perturbed parameters

Cited by 7 publications

References 14 publications

Robust stability and performance analysis of feedback control for plants with uncertain parameters in an ellipsoid

Robust stability and performance analysis of feedback control for plants with uncertain parameters in an ellipsoid

A New Approach to Mixed H₂/H_∞ Optimal PI/PID Controller Design

Stability and D -stability of the family of real polynomials

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Value sets of polynomial families with coefficients depending nonlinearly on perturbed parameters

Cited by 7 publications

References 14 publications

Robust stability and performance analysis of feedback control for plants with uncertain parameters in an ellipsoid

Robust stability and performance analysis of feedback control for plants with uncertain parameters in an ellipsoid

A New Approach to Mixed H2/H∞ Optimal PI/PID Controller Design

Stability and D -stability of the family of real polynomials

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A New Approach to Mixed H₂/H_∞ Optimal PI/PID Controller Design