Haar-Based Stability Analysis of LPV Systems

Araújo, Leonardo Oliveira de; Pellanda, Paulo César; Galdino, Juraci Ferreira; Simões, Alberto M.

doi:10.1109/tac.2014.2322436

Cited by 7 publications

(4 citation statements)

References 16 publications

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“…Generally, two types of orthogonal base of functions are considered in the literature: piecewise orthogonal functions such as Walsh [15], Haar wavelets [16], and Block pulse functions [17] and orthogonal polynomials such as Legendre [18], 2 Mathematical Problems in Engineering Chebyshev [19], and Lagerre polynomials [20]. In [21] authors used Chebyshev polynomials and expanded linear systems in that base to determine the time optimal control input.…”

Section: Introductionmentioning

confidence: 99%

Time Optimal Control Laws for Bilinear Systems

Bichiou

Bouafoura

Braïek

2018

Mathematical Problems in Engineering

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The aim of this paper is to determine the feedforward and state feedback suboptimal time control for a subset of bilinear systems, namely, the control sequence and reaching time. This paper proposes a method that uses Block pulse functions as an orthogonal base. The bilinear system is projected along that base. The mathematical integration is transformed into a product of matrices. An algebraic system of equations is obtained. This system together with specified constraints is treated as an optimization problem. The parameters to determine are the final time, the control sequence, and the states trajectories. The obtained results via the newly proposed method are compared to known analytical solutions.

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Section: Introductionmentioning

confidence: 99%

Time Optimal Control Laws for Bilinear Systems

Bichiou

Bouafoura

Braïek

2018

Mathematical Problems in Engineering

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“…Up to now, most of the existing literatures on stability of LPV systems centralize on Lyapunov asymptotic stability, which is defined over an infinite‐time interval . However, in many practical applications, the main concern is the transient performance of the system over a fixed short time interval.…”

Section: Introductionmentioning

confidence: 99%

“…The stability analysis and delay-dependent H 1 control synthesis for LPV systems with parameter-varying time delays are considered in [15,16]. Also, in [17], a gain-scheduled guaranteed cost control for LPV systems with time-varying state and input delays is presented.Up to now, most of the existing literatures on stability of LPV systems centralize on Lyapunov asymptotic stability, which is defined over an infinite-time interval [18,19]. However, in many practical applications, the main concern is the transient performance of the system over a fixed short time interval.…”

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confidence: 99%

Finite‐time control for LPV systems with parameter‐varying time delays and exogenous disturbances

Duan

Tan

2017

Intl J Robust & Nonlinear

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Summary In this paper, we consider the stability analysis and control synthesis of finite‐time boundedness problems for linear parameter‐varying (LPV) systems subject to parameter‐varying time delays and external disturbances. First, the concepts of uniform finite‐time stability and uniform finite‐time boundedness are introduced to LPV systems. Then, sufficient conditions, which guarantee LPV systems with parameter‐varying time delays finite‐time bounded, are presented by using parameter‐dependent Lyapunov–Krasovskii functionals and free‐weight matrix technologies. Moreover, on the basis of the results on the uniform finite‐time boundedness, the parameter‐dependent state feedback controllers are designed to finite‐time stabilize LPV systems. Both analysis and synthesis conditions are delay‐dependent, and they are formulated in terms of linear matrix inequalities by using efficient interior‐point algorithms. Finally, results obtained in simulation demonstrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.

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“…In contrast, the second strategy is based on synthesis conditions where the controller and filter matrices are scheduled by the timevarying parameters. Known as gain-scheduled (SHAMMA; ATHANS, 1991;APKARIAN et al, 2000;LEITH;LEITHEAD, 2000;RUGH;SHAMMA, 2000;KVIESKA et al, 2009;DE ARAÚJO et al, 2015;BANDEIRA et al, 2018), this technique clearly demands a more involved implementation since the time-varying parameters need to be available online to update the gains but, as benefit, improved performance is possible, in general being at least no more conservative when compared to the robust paradigm (BARBOSA et al, 2002;DE SOUZA et al, 2007;DE CAIGNY et al, 2010;DE CAIGNY et al, 2012;LACERDA et al, 2016;ROSA et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Contributions to filter and control desing for LPV systems using LMIs

Matias Palma Olate

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Los agradecimientos son realizados en Español, mi lengua madre.Como preámbulo, agradezco en primer lugar a mi familia con énfasis en mis tías, Sara y Bernardita, apoyo constante durante mi vida. A mis hermanos, padres y abuela los cuales me ayudan en la crianza de mi hija. Agradezco a Vanessa compañera de vida y madre de mi hija, pilar fundamental en largas horas de trabajo, cuando las cosas no resultaban de todo bien.Referente al desarrollo del presente trabajo, en primer lugar; agradezco a mis orientadores de pre-grado Cristian Duran-Faundez y de mestrado Alim Pedro de Castro Gonçalves, peldaños fundamentales en mi formación profesional.Agradezco a Ricardo C. L. F. Oliveira por haberme aceptado como su primer alumno de doctorado y brindar consejos tanto de preparación de café, conversaciones de temas de actualidad y teoría de control. Agradezco a Cecília de Freitas Morais co-orientadora estricta, rigurosa e inclemente guía, permitiendo calidad en los trabajos realizados. Cecília es un ejemplo de seguir para mi hija y mis futuros orientados como investigadora y a nivel personal.Agradezco a Leonardo de Paula Carvalho amigo, compañero de mestrado y uno de los mas importantes co-investigadores en mis trabajos. Gracias por el tiempo dedicado en todos estos años, en corto "você e Solid Snake do controle". Igualmente, a todos mis compañeros de laboratorio, mestrado e doutorado, y mis coautores de los artículos publicados. Los cuales son muchos para enumerar en una plana, les agradezco a cada uno de ellos.Por último, a Ignacia mi hija, "motor inmóvil" de todo este trabajo.FIN.

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Haar-Based Stability Analysis of LPV Systems

Cited by 7 publications

References 16 publications

Time Optimal Control Laws for Bilinear Systems

Time Optimal Control Laws for Bilinear Systems

Finite‐time control for LPV systems with parameter‐varying time delays and exogenous disturbances

Contributions to filter and control desing for LPV systems using LMIs

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