The LMI control toolbox

Gahinet, Pascal; Nemirovski, Arkadi; Laub, Alan J.; Chilali, M.

doi:10.1109/cdc.1994.411440

Cited by 1,186 publications

(1,313 citation statements)

References 11 publications

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“…O principal resultado é que o ótimo do problema é obtido, quando existir uma solução factível, com menor esforço computacional. Isto acontece, pois as LMIs podem ser facilmente resolvidas utilizando-se algoritmos de convergência polinomial disponíveis na literatura ( (Gahinet et al, 1995), (Oliveira, 1999)). Exemplos ilustraram a viabilidade da metodologia proposta.…”

Section: Introductionunclassified

Metodologia para rastreamento com modificação dos zeros e rejeição de distúrbio aplicada a sistemas incertos

Assunção

Andrea

Teixeira

et al. 2008

Sba Controle & Automação

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The methodology for tracking system and disturbance rejection considering polytopic uncertainties in the plant is proposed in this work. The process of disturbance rejection is make though of the dynamic feedback of the system using a controller K p (s) that minimize the H 2 -norm guaranteed cost from w(t) para z(t), where w(t) is the disturbance signal and z(t) is the output of the system. And so, one use the optimal zeros modification with purpose of to design the tracking system. In this way, the modification of the zeros is used to minimize the H ∞ -norm guaranteed cost from the reference input signal to the tracking error signal, where the tracking error signal was diference between the reference input signal and output signal of the system. The design is formulated in Linear Matrix Inequality (LMI) framework, when it presents a solution, the optimal solution of the stated control problem is obtained. Two practical examples illustrate the effectiveness of the proposed method. RESUMOPropõe-se uma metodologia para rastreamento de sinais e rejeição a distúrbio aplicada a sistemas incertos, com incerteza do tipo politópica. Realiza-se o processo de atenuação do efeito do sinal de distúrbio na saída do sistema através da realimentação dinâmica da saída utilizando-se um controlador K p (s) que minimiza a norma H 2 de custo garantido de w(t) para z(t), sendo w(t) o sinal de distúrbio e z(t) a saída do sistema. Então, para o rastreamento de sinais utiliza-se a modificação ótima dos zeros a fim de minimizar a norma H ∞ de custo garantido da função de transferência entre o sinal de referência e o sinal de erro de rastreamento, sendo o erro de rastreamento a diferença entre o sinal de referência r(t) e o sinal de saída z(t). O projeto de rastreamento de sinais e rejeição do efeito do ruído presente na planta é descrito na forma de LMIs que, quando factíveis, pode-se obter a solução ótima para o problema. Exemplos ilustram a viabilidade da metodologia proposta.

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Section: Introductionunclassified

Metodologia para rastreamento com modificação dos zeros e rejeição de distúrbio aplicada a sistemas incertos

Assunção

Andrea

Teixeira

et al. 2008

Sba Controle & Automação

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“…Then, the equation (52) is a sub-block of (58), so, it is logical to always have γ min ≤ γ o . Moreover, to solve this convex optimisation problem, software like MATLAB's LMI Control Toolbox Gahinet et al (1995) is available to find γ, P and W 1 . Then, now we can calculate …”

Section: A E T F F T Tq ζ T Y Umentioning

confidence: 99%

Robust fault reconstruction based on sliding mode observer for a class of uncertain time-varying delay systems: a rocket motor system application

Boulaabi¹,

Sellami²,

Hmida³

2017

IJAAC

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Abstract:In this paper, we present an extended sliding mode observer (SMO) design method for robust actuator fault reconstruction for a class of linear uncertain delayed systems. The uncertainty considered is matched and bounded. In meantime, the time-varying delay is unknown, bounded and affects simultaneously the input and the state of the system. Using the H1 concept and applying the equivalent output error injection idea from previous works in fault detection and isolation (FDI) scheme, the estimate actuator fault signal is designed with the proposed observer by minimising the uncertainty and the time-varying delay effects. Therefore, this problem is solved via a bounded real lemma (BRL) and the linear matrix inequalities (LMIs) optimisation. A rocket motor system is included to illustrate the efficiency of the proposed method. Even, in the presence of the uncertainty and the time-varying delay, the results of the simulation demonstrate that the proposed schemes can successfully estimate the system states and reconstruct the unknown actuator fault.

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“…The problem defined in (9) - (11) is a convex optimization problem and can be solved using standard LMI solvers [21]. …”

Section: Stability Criterion For Node Level Systemmentioning

confidence: 99%

Decentralised static output feedback stabilisation and synchronisation of networks

Menon

Edwards

2009

Automatica

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In this paper global stabilisation of a complex network is attained by applying local decentralized output feedback control to a minimum number of nodes of the network. The stabilisation of the network is treated as a rank constrained problem. Strict positive realness conditions on the node level dynamics allow nonlinearities/uncertainties which satisfy sector conditions to be considered. A network of Chua oscillators with 75 nodes is considered to demonstrate the efficacy of the approach.

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The LMI control toolbox

Abstract: This paper describes a new MATLAB-based toolbox for control design via linear matrix inequality (LMI) tecliniques. After a brief review of LMIs and of some 01 their applications to control, the toolbox contents and capabilities are presented.

Cited by 1,186 publications

References 11 publications

Metodologia para rastreamento com modificação dos zeros e rejeição de distúrbio aplicada a sistemas incertos

Metodologia para rastreamento com modificação dos zeros e rejeição de distúrbio aplicada a sistemas incertos

Robust fault reconstruction based on sliding mode observer for a class of uncertain time-varying delay systems: a rocket motor system application

Decentralised static output feedback stabilisation and synchronisation of networks

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