Finite frequency $$H_\infty $$ H ∞ control of 2-D continuous systems in Roesser model

Duan, Zhaoxia; Xiang, Zhengrong

doi:10.1007/s11045-016-0430-3

Cited by 22 publications

(13 citation statements)

References 33 publications

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“…Moreover, based on Lemma 5, FF BRLs for 2D continuous/discrete state‐delay Roesser systems, which are detailed in the following, can be presented similarly. Thus, combining with Lemma 5, it is easy to see that results in the paper generalise the the existing FF BRL for 2D continuous/discrete/continuous‐discrete Roesser system in [9, 25, 31] in two aspects: the frequency range (from low frequency range to a given frequency interval) and the class of system (generalised to uncertain state‐delay Roesser systems).…”

Section: Ff Brls and Ff Prls For Uncertain 2d Roesser Systems With supporting

confidence: 56%

“…Comparing with the classical BRL and PRL, FF BRLs and FF PRLs help in discussing the positive realness and the bounded realness on finite frequency ranges, which is more common in practical engineering applications. Moreover, as discussed in Remark 2, Corollary 3 also is a generalisation of the existing FF PRLs for 2D continuous/discrete/continuous‐discrete Roesser systems in [9, 25, 31].…”

Section: Ff Brls and Ff Prls For Uncertain 2d Roesser Systems With mentioning

confidence: 77%

“…□ Remark 1 Lemma 5 establishes an equivalence between FDIs (

Γ_{λ} {scriptT}_{ζ} ζ = 0

) and LMIs (

t r ()(, ζ ζ^{*} M_{λ}) \geq 0

). it is worthwhile to point out that, let

ϖ_{l_{1}} = - ϖ_{l_{2}} false(l = h, v false)

, the existing results in [9, 25, 31] can be straightforward obtained by Lemma 5. In other words, with the help of the special sets

Ξ_{ζ}

and

Ξ_{M}

, Lemma 5 covers FDIs in finite frequency intervals for 2D continuous/discrete/continuous‐discrete settings.…”

Section: Ff Brls and Ff Prls For Uncertain 2d Roesser Systems With mentioning

confidence: 99%

“…Recently, some results have addressed this issue and generalised the standard Kalman‐Yakubivich‐Popov lemma [23] to both one‐dimensional (1D) systems and multi‐dimensional ( n ‐D) systems [9, 24–27]. Based on the generalised KYP (GKYP) lemma, which is used to directly transfer the FDI over the finite frequency range to an equivalent linear matrix inequality (LMI), many control problems in finite frequency range have been studied [7, 9, 13, 27–31].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

Wang

et al. 2018

IET Control Theory & Applications

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Section: Ff Brls and Ff Prls For Uncertain 2d Roesser Systems With supporting

confidence: 56%

Section: Ff Brls and Ff Prls For Uncertain 2d Roesser Systems With mentioning

confidence: 77%

“…□ Remark 1 Lemma 5 establishes an equivalence between FDIs (

Γ_{λ} {scriptT}_{ζ} ζ = 0

) and LMIs (

t r ()(, ζ ζ^{*} M_{λ}) \geq 0

). it is worthwhile to point out that, let

ϖ_{l_{1}} = - ϖ_{l_{2}} false(l = h, v false)

, the existing results in [9, 25, 31] can be straightforward obtained by Lemma 5. In other words, with the help of the special sets

Ξ_{ζ}

and

Ξ_{M}

, Lemma 5 covers FDIs in finite frequency intervals for 2D continuous/discrete/continuous‐discrete settings.…”

Section: Ff Brls and Ff Prls For Uncertain 2d Roesser Systems With mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

Wang

et al. 2018

IET Control Theory & Applications

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“…Recently, the generalized KYP lemma has been extended to 2D systems. To name a few, the generalized KYP lemmas for 2D discrete, continuous and continuous–discrete systems described by the Roesser model were investigated in Yang et al (2008), Wang et al (2015) and Duan and Xiang (2016), respectively. Based on the work by Yang et al (2008), the problem of robust FF H ∞ filtering for 2D discrete Roesser systems was addressed by the generalized KYP lemmas in Li and Gao (2012).…”

Section: Introductionmentioning

confidence: 99%

Finite frequency H∞ filtering for uncertain two-dimensional continuous systems

Wang

Qin

2018

Transactions of the Institute of Measurement and Control

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This paper investigates the problem of robust finite frequency (FF) [Formula: see text] filtering for two-dimensional (2D) continuous systems described by the Roesser state-space model with norm-bounded uncertainties. A further generalized Kalman–Yakubivich–Popov (KYP) lemma for 2D continuous Roesser systems is presented in a unified form. By the given generalized KYP lemma, the problem of standard [Formula: see text] filtering for uncertain 2D continuous Roesser systems is extended to the FF case. Finally, an illustrative example is provided to validate the effectiveness of the proposed method.

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Dynamic event‐triggered control of 2‐D continuous systems in Roesser model

Hu,

Meng,

Huang

2024

Asian Journal of Control

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In this paper, a dynamic event‐triggered control problem is discussed for 2‐D continuous systems by the Roesser model. In order to reduce communication frequency and avoid dependence on global information, a dynamic event‐triggered mechanism is constructed, which is more flexible than some existing event‐triggered schemes with fixed event‐triggered thresholds. Utilizing the dynamic event‐triggered mechanism, a state feedback controller is designed. By constructing a 2‐D Lyapunov function, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are firstly established such that the 2‐D system is asymptotically stable with a disturbance attenuation performance. It is also proved that the Zeno phenomenon is excluded. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

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Finite frequency $$H_\infty $$ H ∞ control of 2-D continuous systems in Roesser model

Cited by 22 publications

References 33 publications

Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

Finite frequency H∞ filtering for uncertain two-dimensional continuous systems

Dynamic event‐triggered control of 2‐D continuous systems in Roesser model

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