Common diagonal Lyapunov function for third order linear switched system

Büyükköroğlu, Taner

doi:10.1016/j.cam.2011.06.013

Cited by 10 publications

(4 citation statements)

References 9 publications

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“…However, in some cases conditions are known that guarantee the existence of a CLS; a very good survey about this may be found in [17]. Despite the large amount of work that has been done on this subject, the CLS existence problem is still challenging and and keeps attracting the attention of several researchers, see for instance [4,7,10].…”

Section: Elamentioning

confidence: 99%

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A note on simultaneous block diagonally stable matrices

Brás¹,

Carapito²,

Rocha³

2013

ELA

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Abstract. Consider a set of square real matrices of the same size A = {A 1 , A 2 , . . . , A N }, where each matrix is partitioned, in the same way, into blocks such that the diagonal ones are square matrices. Under the assumption that the diagonal blocks in the same position have a common Lyapunov solution, sufficient conditions for the existence of a common Lyapunov solution with block diagonal structure for A are presented. Furthermore, as a by-product, an algorithm for the construction of such a common Lyapunov solution is proposed.

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Section: Elamentioning

confidence: 99%

“…A set of matrices is said to be simultaneous diagonally stable if it admits a diagonal CLS. Diagonal stability has been used in several applications, see [9], for a good survey, and, for more recent research on this notion; see for instance [2,4,15].…”

Section: Elamentioning

confidence: 99%

A note on simultaneous block diagonally stable matrices

Brás¹,

Carapito²,

Rocha³

2013

ELA

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“…3 × 3. Next, applying the same result of Redheffer on B and C, the problem is eventually reduced to determining a CDLS for the four 2 × 2 matrices B [ 2 ], B/B[{3}], C [ 2 ], and…”

Section: Introductionmentioning

confidence: 99%

“…As pointed out in [12], CDLS's arise naturally on interconnected time-varying and switched systems. For recent works on these and related topics, see, for example, [2,12,14,17,18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On common diagonal Lyapunov solutions

Gümüş

2016

Linear Algebra and its Applications

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Several recent results regarding common diagonal Lyapunov solutions are further explored here. The first one, attributed to Redheffer and revisited by Shorten and Narendra, reduces the diagonal stability of a matrix to common diagonal Lyapunov solutions on two matrices of order one less. We present a shorter, purely matrix-theoretic proof of this result along with its extensions. The second one concerns two different necessary and sufficient conditions, due to Oleng, Narendra, and Shorten, for a pair of 2 × 2 matrices to share a common diagonal Lyapunov solution. We show that these two conditions are connected directly to each other.

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