A simpler formula for the singular values of a certain Hankel operator

Özbay, Hitay

doi:10.1016/0167-6911(90)90061-x

Cited by 15 publications

(6 citation statements)

References 12 publications

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“…Then, we have an invertible relation between the free parameters Q1X and QX in H∞. Note that the problem (23) is exactly in the form (13) except that Q1X (s) is restricted to have Q1X (pi) = X(pi) = 1/N (pi), whereas in (13) there is no such restriction on the free parameter Qi ∈ H∞. In summary, we have the following…”

Section: T1(s) = N (S)(x(s) + Di(s)q1(s))mentioning

confidence: 95%

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Integral Action Controllers for Systems with Time Delays

Özbay

Gündeş

2009

Topics in Time Delay Systems

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Summary. Consider a stabilizing controller C1 for a given plant P . If C1 and P do not have any zeros at the origin, then one can use a cascade connected PI (proportional plus integral) controller Cpi with C1 and keep the feedback system stable. In this work we examine the allowable range of the integral action gain in Cpi, and discuss how C1 should be chosen to maximize this range for systems with time delays.

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Section: T1(s) = N (S)(x(s) + Di(s)q1(s))mentioning

confidence: 95%

“…For a general inner function Pi, the problem (14) can be solved using the techniques developed for the H∞ control of infinite dimensional systems, see e.g. [6,10,13] and their references. It turns out that the optimal Qi is in the form…”

Section: Stable Plantsmentioning

confidence: 99%

Integral Action Controllers for Systems with Time Delays

Özbay

Gündeş

2009

Topics in Time Delay Systems

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“…Weighted sensitivity minimization for time delay systems was the first H 1 control problem solved for infinite dimensional systems, [1][2][3]. The methods used in [2,3] were extended to cover a larger class of distributed parameter systems in [4][5][6][7][8][9]. Another type of H 1 control problem studied for delay systems was robust stabilization in the gap metric, [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…In these papers, the optimal performance level and the corresponding controller are obtained by studying a "Hankel+Toeplitz", or a "skew-Toeplitz" operator, [15][16][17]. However, with the exception of [7,10] (both of them deal with one-block problems) explicit formula for the controller could not be given in the previous cited papers. One needed to follow a complicated substitutions and transformations to arrive at the controller from the singular vectors of the related operators.…”

Section: Introductionmentioning

confidence: 99%

Computation of H_∞ controllers for infinite dimensional plants using numerical linear algebra

Özbay

2012

Numerical Linear Algebra App

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The mixed sensitivity minimization problem is revisited for a class of single-input-single-output unstable infinite dimensional plants with low order weights. It is shown that H 1 controllers can be computed from the singularity conditions of a parameterized matrix whose dimension is the same as the order of the sensitivity weight. The result is applied to the design of H 1 controllers with integral action. Connections with the so-called Hamiltonian approach are also established.

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“… The rational single‐input–single‐output ( SISO ) system with an input/output ( I / O ) time‐delay :The optimal ℋ︁ ∞ controller is designed in 4, 5 using operator theoretic methods; see also 6, 7 and the references therein. State‐space solution to the same problem is given in 8, 9.…”

Section: Introductionmentioning

confidence: 99%

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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A simpler formula for the singular values of a certain Hankel operator

Cited by 15 publications

References 12 publications

Integral Action Controllers for Systems with Time Delays

Integral Action Controllers for Systems with Time Delays

Computation of H_∞ controllers for infinite dimensional plants using numerical linear algebra

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

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A simpler formula for the singular values of a certain Hankel operator

Cited by 15 publications

References 12 publications

Integral Action Controllers for Systems with Time Delays

Integral Action Controllers for Systems with Time Delays

Computation of H ∞ controllers for infinite dimensional plants using numerical linear algebra

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

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Product

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Computation of H_∞ controllers for infinite dimensional plants using numerical linear algebra