Differential Linear Matrix Inequalities Optimization

Gonçalves, Tiago R.; Gabriel, Gabriela W.; Geromel, J.C.

doi:10.1109/lcsys.2018.2884016

Cited by 17 publications

(6 citation statements)

References 11 publications

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“…É importante notar que o método para a obtenção da solução da DLMI (10) é idêntico ao apresentado em Gonçalves et al (2019), podendo, para isso, ser utilizada qualquer ferramenta de resolução de LMI disponível na literatura. Ainda de Geromel et al (2019), a solução de (10) pode ser escrita na forma Teorema 2 Seja T > 0, um período de amostragem constante e γ 2 > 0 dados.…”

Section: Discussão Preliminarunclassified

“…Resultado similar, adaptado para os sistemas lineares com saltos markovianos, é apresentado em Gabriel (2016). Em Gonçalves et al (2019), é apresentada a resolução de problemas baseados em DL-MIs (Differential Linear Matrix Inequalities), resultantes da otimização de sistemas híbridos nos contextos da minimização das normas H 2 e H ∞ através de LMIs. Em Gabriel and Geromel (2018) e Gabriel and Geromel (2021), são apresentadas extensões deste problema no contexto de sistemas não lineares e de controle baseado na norma H 2 .…”

Section: Introductionunclassified

“…Para isso, vamos considerar o sismedir o primeiro estado do sistema, com ruído, e gostaríamos de estimar o segundo estado. Desta forma, as matrizes que definem a saída medida e de controle sãoC y = 1 0 , E d = 1; C z = 0 1Para a resolução das LMIs utilizamos a técnica proposta emGonçalves et al (2019), em que a matriz P (t) é considerada linear por partes dividida em 16 intervalos em [0, T ]. Tomando alguns valores de T > 0, a Figura 1 mostra que o problema de observação é factível, com valores crescentes…”

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Projeto de um observador de estados para sistemas lineares amostrados através de condições LMI

Pereira

Gabriel

Oliveira

2021

Procedings Do XV Simpósio Brasileiro De Automação Inteligente

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This paper presents the Luenberger's state observer design problem applied to continuous-time systems whose measured output is sampled in time. To solve this problem, a continuous-time structure for the state observer is considered in the context of the minimization of a performance index which leads to the evaluation of the H 2 and H∞ norm. The hybrid approach together with a two-point boundary value problem is the main key to obtain sufficient convex conditions expressed through LMIs (Linear Matrix Inequalities) for the observer design problem. Finally, a numerical example is presented to illustrate the results.

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Section: Discussão Preliminarunclassified

Section: Introductionunclassified

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Projeto de um observador de estados para sistemas lineares amostrados através de condições LMI

Pereira

Gabriel

Oliveira

2021

Procedings Do XV Simpósio Brasileiro De Automação Inteligente

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“…This approach is efficient if the IQC is parameterized by a small number of variables. A thorough computational comparison between this ellipsoidal method and more recent DLMI algorithms [14][15][16] is needed and will be part of future work.…”

Section: Introductionmentioning

confidence: 99%

“…This heuristic has been used for both LTV 8‐11 and linear parameter varying (LPV) systems 12,13 . More recent work on DLMIs includes 14‐16 . It is notable that 14 includes a global convergence result (Theorem 1) as the number of time points goes to infinity.…”

Section: Introductionmentioning

confidence: 99%

Trajectory‐based robustness analysis for nonlinear systems

Seiler,

Venkataraman

2023

Intl J Robust & Nonlinear

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This article considers the robustness of an uncertain nonlinear system along a finite‐horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients. First, the nonlinear system is approximated by a linear time‐varying (LTV) system via linearization along a trajectory. This linearization introduces an additional forcing input due to the nominal trajectory. Second, the input/output behavior of the perturbation is described by time‐domain, integral quadratic constraints (IQCs). Third, a dissipation inequality is formulated to bound the worst‐case deviation of an output signal due to the uncertainty. These steps yield a differential linear matrix inequality (DLMI) condition to bound the worst‐case performance. The robustness condition is then converted to an equivalent condition in terms of a Riccati differential equation. This yields a computational method that avoids heuristics often used to solve DLMIs, for example, time gridding. The approach is demonstrated by a two‐link robotic arm example.

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