On strong regular stabilizability for linear neutral type systems

Rabah, Rabah; Sklyar, Grigory M.; Rezounenko, Alexander V.

doi:10.1016/j.jde.2008.02.041

Cited by 30 publications

(45 citation statements)

References 17 publications

(53 reference statements)

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“…(1). Using Theorem 8 from [16] to both scalar equations we get that for any sequence τ (k) quadratically close to sequenceλ ,…”

Section: Example 21 We Consider Eq (1) Withmentioning

confidence: 99%

“…Operator A 1 generates a C 0 -semigroup and also is of the form (3) with the same matrix A −1 and disturbed A 2 , A 3 (see [16] for more details). Thus assertion follows directly from Theorem 2.1.…”

Section: Statement 41 Let Us Consider a Control System (31) If Thermentioning

confidence: 99%

“…O'Connor, T.J. Tarn [11], R. Rabah, G.M. Sklyar [12,13], R. Rabah et al [16], S.M. Verduyn Lunel, D.V.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Growth of Solutions of Neutral Type Systems

Sklyar

Polak

2013

Appl Math Optim

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We consider a differential system of neutral type with distributed delay.We obtain a precise norm estimation of semigroup generated by the operator corresponding to the system in question. Our result is based on a spectral analysis of the operator and some uniform estimation of norms of the exponentials of matrices. We also discuss the stability properties of corresponding solutions and the existence of the fastest growing solution.

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“…(1). Using Theorem 8 from [16] to both scalar equations we get that for any sequence τ (k) quadratically close to sequenceλ ,…”

Section: Example 21 We Consider Eq (1) Withmentioning

confidence: 99%

Section: Statement 41 Let Us Consider a Control System (31) If Thermentioning

confidence: 99%

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Asymptotic Growth of Solutions of Neutral Type Systems

Sklyar

Polak

2013

Appl Math Optim

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“…Such a situation may occur for hyperbolic equations or delay equations of neutral type (e.g. Rabah et al [13,14]). …”

Section: Introductionmentioning

confidence: 99%

“…First we give the proof of Theorem 1.1 preceded by several technical results. Next section is devoted to the analysis of stability of neutral type equations (3) and regular feedback stabilizability of these equations [14]. In the appendix we give two simple statements about complex matrices, which are used in our work.…”

Section: Introductionmentioning

confidence: 99%

On Asymptotic Estimation of a Discrete Type $$C_0$$ C 0 -Semigroups on Dense Sets: Application to Neutral Type Systems

Sklyar

Polak

2016

Appl Math Optim

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We consider an abstract Cauchy problem for a certain class of linear differential equations in Hilbert space. We obtain a criterion for stability on some dense subsets of the state space of the C 0 -semigroups in terms of location of eigenvalues of their infinitesimal generators (so-called polynomial stability). We apply this result to analysis of stability and stabilizability of special class of neutral type systems with distributed delay.

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Coprime‐inner/outer factorization of SISO time‐delay systems and FIR structure of their optimal H‐infinity controllers

Gümüşsoy¹

2011

Intl J Robust & Nonlinear

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The approach in Foias et al. (Robust control of Infinite Dimensional: Frequency Domain Methods. Springer: Berlin, 1996) is one of the well-developed methods to design H-infinity controllers for general infinite dimensional systems. This approach is applicable if the plant admits a special coprime-inner/outer factorization. We give the largest class of single-input-single-output (SISO) time-delay systems for which this factorization is possible and factorize the admissible plants. Based on this factorization, we compute the optimal H-infinity performance and eliminate unstable pole-zero cancellations in the optimal H-infinity controller. We extend the results on the finite impulse response structure of optimal H-infinity controllers by showing that this structure appears not only for plants with input/output delays, but also for general SISO time-delay plants.This establishes the connection between an asymptotic chain root of q(s), r q,i and the corresponding root of its asymptotic polynomial p(s), r p,i as r q,i = 0 +j i ⇐⇒ r p,i = e −( 0 +j i )/N .The real part of r q,i is negative, o < 0, if and only if the magnitude of the root of the asymptotic polynomial p(s) is greater than 1, |r p,i | > 1. The assertion follows.Given a neutral quasi-polynomial with infinitely many roots inside C + , its conjugate quasipolynomial may have finitely many roots inside C + . This class of neutral quasi-polynomials plays 984

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On strong regular stabilizability for linear neutral type systems

Cited by 30 publications

References 17 publications

Asymptotic Growth of Solutions of Neutral Type Systems

Asymptotic Growth of Solutions of Neutral Type Systems

On Asymptotic Estimation of a Discrete Type $$C_0$$ C 0 -Semigroups on Dense Sets: Application to Neutral Type Systems

Coprime‐inner/outer factorization of SISO time‐delay systems and FIR structure of their optimal H‐infinity controllers

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