Expansion of det(A+B) and robustness analysis of uncertain state space systems

Xu, Shengyuan; Darouach, Mohamed; Schaefers, J.

doi:10.1109/9.262036

Cited by 29 publications

(10 citation statements)

References 25 publications

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“…Matrix Y is stable since G i0 is constant, and F ei , if properly designed, is stable. According to Xu et al [20], det(I + ZY) can be expressed as…”

Section: Stability Analysis Of Mtdc Systemsmentioning

confidence: 99%

“…VSC 1 and VSC 2 are in PC mode with power set points equal to zero. Then, y 3 0 = 2.4∠ − 123 ∘ pu (Table 2) Using (20), T cr2 = 3.1∠175 ∘ , meaning that T will cross the real axis at around −3. Similarly to the first resonance case, the values of re[T cr ] indicate in both cases a high risk of instability.…”

Section: Stability Analysis With Respect To the Second Resonancementioning

confidence: 99%

“…Note that, in this case, the magnitude of the oscillations is more pronounced in voltages e 3 and e 4 compared with e 1 and e 2 . Again, according to (20), one way to improve the system stability is to turn either re[y 3 ] or re[y 4 ] (or both together) positive. In this case, this is achieved by turning VSC 3 to DVC mode due to the fact that ∥ z 33 cr ∥ pu has the greatest impact (see Table 3).…”

Section: Simulation Verificationsmentioning

confidence: 99%

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Methodology for the analysis of dc‐network resonance‐related instabilities in voltage‐source converter‐based multi‐terminal HVDC systems

Pinares¹,

Bongiorno²

2017

IET Generation, Transmission & Distribution

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“…Matrix Y is stable since G i0 is constant, and F ei , if properly designed, is stable. According to Xu et al [20], det(I + ZY) can be expressed as…”

Section: Stability Analysis Of Mtdc Systemsmentioning

confidence: 99%

Section: Stability Analysis With Respect To the Second Resonancementioning

confidence: 99%

Section: Simulation Verificationsmentioning

confidence: 99%

See 1 more Smart Citation

Methodology for the analysis of dc‐network resonance‐related instabilities in voltage‐source converter‐based multi‐terminal HVDC systems

Pinares¹,

Bongiorno²

2017

IET Generation, Transmission & Distribution

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“…Really, it can be noticed that for all the three examples of [l] the frequency characteristics of G( z ) and G: ( 2 ) are not distinguishable, but the plot of GT in Fig. l e ) .…”

Section: U Answer To the First Questionmentioning

confidence: 99%

Expansion of det(A+B+C) and robustness analysis of discrete-time state-space systems

Darouach²,

Schaefers

1995

IEEE Trans. Automat. Contr.

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Since the biases caused by noise can be eliminated, then the problem of set-membership identification turns to be a problem of a model fitting, the same as for a deterministic linear system. If we increase the degree of the nominal part of the system and at the same time weaken the unmodeled dynamics, then the estimated bound of the parameters set will be reduced, and a more accurate estimation of the system can be reached. It is worthy to notice that the method presented here needs no any previous knowledge of the noise model. REFERENCES [l] E. Fogel, "System identification via membership set constrains with energy constrained noise," IEEE Tmns. Auromat. Contr., vol. AC-24, [2] R. L. Kosut, M. K. Lau, and S. P. Boyd, "Set-membership identification of systems with parametric and nonparametric uncertainty ," IEEE Trans. Automat. Contr., vol. 37, pp. 929-941, 1992. [3] R. C. Younce and C. E. Rohrs, "Identification w i t h nonparametric uncertainty," [4] C.-B. Feng and W.-X. Zheng, "On-line modified least-squares parameter estimation of hear systems with input-output data polluted by measurement noise," in Pmc, 8th IFAC Symp. Identification, System and Parameter Esrimation, Absftaet-h this paper, the expansion of det( A + B + C) is given. The robustness problem for discrete-time state-space systems with uncertain parameters is investigated by applying the Sehw stability theory of interval polynomials. A stability robustness criterion for the uncertain systems is derived. Illustrative exampks are presented.

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“…Robust stability (RS) analysis determines the pole of the polynomial or the eigenvalues of the matrix in the left half-plane (Chapellat, Dahleh, and Bhattacharyya 1991;Dahleh, Tesi, and Vicino 1993;Hollot and Tempo 1994;Jaulin et al 2001;Walter and Jaulin 1994), whereas performance analysis is more general. Notable examples of issues considered in performance analysis include disturbance attenuation, noise rejection, and relative stability, which, collectively, are commonly referred to as robust damping-cone stability (RDCS) (Dahleh, Tesi, and Vicino 1992;Khadraoui, Rakotondrabe, and Lutz 2012;Rakotondrabe 2011;Wang 2002;Xu, Darouach, and Schaefers 1993;Xu, Rachid, and Darouach 1998). Conventional research methods are direct or indirect; the former involve solving determining polynomials or eigenvalues of matrices, while the latter apply a stability criterion to determine the stability of the system.…”

Section: Introductionmentioning

confidence: 99%

Robust pole assignment for interval polynomial based on positive interval Routh-table: positive property of Routh-table of binomial coefficients

Juang

2015

Journal of the Chinese Institute of Engineers

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This paper elucidates a robust pole assignment (RPA) scheme for an interval polynomial based on positive interval Routh-table using a binomial coefficients feedback gain. The robust scheme transforms the problem of RPA into the problem of solving a family of stability condition polynomials that have positive function values. The condition for the existence of solution is that all entries of the Routh-table of binomial coefficients (RTBC) are positive. Importantly, this paper provides an advanced general formula for the generated entries of the RTBC, confirming that all entries of RTBC are positive. An illustrative example reveals the effectiveness of the scheme.

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Expansion of det(A+B) and robustness analysis of uncertain state space systems

Cited by 29 publications

References 25 publications

Methodology for the analysis of dc‐network resonance‐related instabilities in voltage‐source converter‐based multi‐terminal HVDC systems

Methodology for the analysis of dc‐network resonance‐related instabilities in voltage‐source converter‐based multi‐terminal HVDC systems

Expansion of det(A+B+C) and robustness analysis of discrete-time state-space systems

Robust pole assignment for interval polynomial based on positive interval Routh-table: positive property of Routh-table of binomial coefficients

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