On necessary conditions for real robust schur-stability

Batra, Prashant

doi:10.1109/tac.2002.808471

Cited by 25 publications

(11 citation statements)

References 4 publications

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“…In particular, the Hurwitz stability [6], [7], the Schur stability [8], [9], and the eigenvalue boundary problem with perturbation [3], [4], [10], [11] have been well studied and formulated. However, some fundamental interval computational problems such as "power of an interval matrix," "analytical stability condition of an interval polynomial matrix," and "maximum singular value bound of an interval matrix " have not yet been well solved.…”

Section: Introductionmentioning

confidence: 99%

Exact Maximum Singular Value Calculation of an Interval Matrix

Ahn

Chen

2007

IEEE Trans. Automat. Contr.

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In this note, we present a method for calculating the maximum singular value of an interval matrix. First, we provide an algorithm for calculating the maximum singular value of a square interval matrix. Then, based on this algorithm, we extend the result to non-square interval matrix case and to the case of computing the minimum singular value. Through numerical examples, the validity of the suggested methods is illustrated. Particularly, we compare the newly-proposed method with an existing method to show that the new method finds the correct bound of the maximum singular value with no exception.Index Terms-Interval matrix, maximum singular value.

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Section: Introductionmentioning

confidence: 99%

Exact Maximum Singular Value Calculation of an Interval Matrix

Ahn

Chen

2007

IEEE Trans. Automat. Contr.

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“…There are many existing research efforts and applications under the term "interval" such as interval algebra [1], [2], Schur stability of interval matrices [3], [4], Hurwitz stability of interval matrices [5], [6], [7], interval polynomial matrices [8], eigenvalues of interval matrices [9], [10], [11], and robust control with parameter uncertainty [12], [13], interval polynomial [14], [15]. By using an effective method for checking the linear independency of interval vector, the robust controllability and un-controllability problems of uncertain interval systems were firstly solved in [16].…”

Section: Introductionmentioning

confidence: 99%

Robust controllability of interval fractional order linear time invariant stochastic systems

Zeng

Chen

Yang

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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We deal with the robust controllability problem of the fractional order linear time invariant (FO-LTI) stochastic systems with interval coefficients. We present a necessary and sufficient condition for the controllability problem for the case when there is no interval uncertainty. Based on the concept of linear independency of interval vectors, we formulate the approach to check the robust controllability of interval FO-LTI stochastic systems by employing some simple but very effective sufficient condition for checking the linear independency of interval vectors. Finally, an illustrative example is presented. We show that this interval FO-LTI stochastic system is weakly controllable, while the corresponding deterministic system without noise perturbation is uncontrollable.

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“…Much research work has been done to approximate the Schur stability domain by boxes [ 3,4 ], ellipsoids [ 5,6 ], polytopes [ 7−9 ] or other convex sets [ 10,11 ]. In [ 12 ] a linear Schur invariant transformation with a free parameter is introduced in the discrete polynomial coefficient space which give us a possibility to generalize polytopic stability conditions such as Cohn's condition [ 1 ], discrete Kharitonov's theorem [ 13 ] and reflection vector polytopes [ 9 ].…”

Section: Introductionmentioning

confidence: 99%

Stability of discrete-time systems via polytopes of reflection vector sets

Avanessov¹,

Nurges²

2012

Estonian J. Eng.

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The stability domain of discrete-time systems is investigated via reflection coefficients of characteristic polynomials of the system. Stable polytopes in the coefficients space of characteristic polynomials are defined starting from the sufficient stability condition in the polynomial reflection coefficients space using different reflection vector sets. The volumes of these stable polytopes are calculated via the triangulation method.

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On necessary conditions for real robust schur-stability

Cited by 25 publications

References 4 publications

Exact Maximum Singular Value Calculation of an Interval Matrix

Exact Maximum Singular Value Calculation of an Interval Matrix

Robust controllability of interval fractional order linear time invariant stochastic systems

Stability of discrete-time systems via polytopes of reflection vector sets

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