Uniform versions of Finsler's lemma

Kussaba, Hugo T. M.; Ishihara, J.Y.; Borges, Renato Alves

doi:10.1109/cdc.2015.7403370

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…This work is an extension of our previous analysis on uniform versions of Finsler's lemma [22]. Here, some new results are presented and some results from [22] were improved: the converse of Lemma 3 from [22] has been proved in Lemma 4 of this paper. Both Lemma 3 and Theorem 2 from [22] were stated for matrix-valued functions of a compact subset of R. In this paper, these results are extended for matrixvalued functions of a compact subset of R d .…”

Section: Introductionmentioning

confidence: 80%

“…In the LMI context, this allows reducing computational burden without increasing the conservatism of the solution. This work is an extension of our previous analysis on uniform versions of Finsler's lemma [22]. Here, some new results are presented and some results from [22] were improved: the converse of Lemma 3 from [22] has been proved in Lemma 4 of this paper.…”

Section: Introductionmentioning

confidence: 80%

“…Both Lemma 3 and Theorem 2 from [22] were stated for matrix-valued functions of a compact subset of R. In this paper, these results are extended for matrixvalued functions of a compact subset of R d . The hypothesis of Theorem 1 and Corollary 1 from [22] has been weakened in Theorem 4 of this work.…”

Section: Introductionmentioning

confidence: 94%

“…Here, some new results are presented and some results from [22] were improved: the converse of Lemma 3 from [22] has been proved in Lemma 4 of this paper. Both Lemma 3 and Theorem 2 from [22] were stated for matrix-valued functions of a compact subset of R. In this paper, these results are extended for matrixvalued functions of a compact subset of R d . The hypothesis of Theorem 1 and Corollary 1 from [22] has been weakened in Theorem 4 of this work.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Existence of Continuous or Constant Finsler's Variables for Parameter-Dependent Systems

Ishihara

Kussaba

Borges

2017

IEEE Trans. Automat. Contr.

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Abstract-Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter dependent LMIs, as such those that arise from problems of robust stability, the extra variables introduced by this lemma also become dependent on this parameter. This technical note presents some sufficient conditions which ensure, without losing generality, that these extra variables can assume a simple functional dependence on the parameters as continuity or even independence. The results allow avoiding an unnecessary use of a more functionally complicated parameter dependent variable that increases the search computational burden without reducing the conservatism of the solution.

show abstract

Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Existence of Continuous or Constant Finsler's Variables for Parameter-Dependent Systems

Ishihara

Kussaba

Borges

2017

IEEE Trans. Automat. Contr.

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“…e Lyapunov theory allows to write the conditions in the form of LMIs and solving them by available computational packages [14,15]. A switched Lyapunov function allows the use of slack variables which are introduced in the problem to lessen the conservativeness [16]. e control gain is recovered from the slack matrices instead of using the Lyapunov matrix.…”

Section: Introductionmentioning

confidence: 99%

State-Feedback Control for Cyber-Physical Discrete-Time Systems under Replay Attacks: An LMI Approach

Moreira

Lacerda

2022

Mathematical Problems in Engineering

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This paper addresses the state-feedback control problem for cyber-physical discrete-time linear systems. The main goal is to design state-feedback controllers that can mitigate the interference of replay attacks in the stability of the closed-loop system. The system under replay attack is modeled as a switched linear system, and a packet-based approach is employed for control design. New conditions in the form of Linear Matrix Inequalities are presented to provide stabilizing controllers. Numerical experiments illustrate the effectiveness of the proposed method.

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New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

Taousser,

Morovati,

Zhang

et al. 2024

Intl J Robust & Nonlinear

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Safety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel‐wind energy system is considered and modeled as a switching system between normal, faulted, and post‐fault modes. A safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33‐bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness.

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Uniform versions of Finsler's lemma

Cited by 5 publications

References 24 publications

Existence of Continuous or Constant Finsler's Variables for Parameter-Dependent Systems

Existence of Continuous or Constant Finsler's Variables for Parameter-Dependent Systems

State-Feedback Control for Cyber-Physical Discrete-Time Systems under Replay Attacks: An LMI Approach

New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

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