Finite-time stability of discrete-time nonlinear systems: analysis and design

Mastellone, Silvia; Dorato, R.; Abdallah, Chaouki T.

doi:10.1109/cdc.2004.1428845

Cited by 26 publications

(14 citation statements)

References 18 publications

(23 reference statements)

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“…In particular, when one requires that the state trajectories stay inside a ball of radius r whenever the initial condition belongs to a ball of radius q, q ≤ r, one has the rather general concept that is employed in [1] and [13]. We quote it here.…”

Section: Introductionmentioning

confidence: 98%

“…These concepts basically require that the state trajectory stays within given bounds over an entire time interval of horizon N . This type of of concept is of interest in many practical situations, and it is not connected to the classical asymptotic or exponential stability concepts in the sense that one neither implies nor excludes the other [13].…”

Section: Introductionmentioning

confidence: 98%

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A finite-time stability concept and conditions for finite-time and exponential stability of controlled nonlinear systems

Costa

Val

2006

2006 American Control Conference

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This paper introduces a finite-time stability concept for nonlinear systems and the corresponding notion of stabilizability of controls. The concept generalizes previous finite-time stability as it requires that the state trajectory satisfies a given bound at some time instant in a certain interval, whereas previous notions considers that the system stays within that bound over the entire interval. Here, the bound on the trajectory may represent a region arbitrarily close to the origin, and thus it is in tune with situations where contractive trajectories are required. This feature allows us to relate the proposed concept with the usual exponential stability concept, and simultaneously, with the previous finitetime concepts, thus clarifying the relations among them. As regards to controlled systems, we derive a sufficient condition for stabilizability, with the interpretation that the size of the time interval demanded by the control to drive the trajectory into a specified region is in inverse proportion with the size of the region. Moreover, we present a simple moving horizon implementation for a stabilizing (in the new sense) control that provides an exponentially stable controlled system. For stationary controls we can connect stabilizability in the sense here with the classical exponential sense. We show that the control is exponentially stabilizing whenever it is finite-time stabilizing and stationary. An illustrative example is included.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

A finite-time stability concept and conditions for finite-time and exponential stability of controlled nonlinear systems

Costa

Val

2006

2006 American Control Conference

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“…The concept of FTS has been revisited recently and discussed for linear and nonlinear systems [14][15][16][17]. A stochastic version of FTS developed in [18] and [19] for analysis of continuous and discrete stochastic system, respectively, and in [20,21] for optimal control design. But in these references, they just discussed the pure stochastic system and did not consider the impulsive and switching behaviors.…”

mentioning

confidence: 99%

Finite-time stability and stabilization of nonlinear stochastic hybrid systems

Yang

Chen

2009

Journal of Mathematical Analysis and Applications

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This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finitetime stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.

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“…As aplicações para SLSM são diversas, dentre as quais citamos, aeronáutica [3], modelos macroeconômicos [23] e receptores térmicos [43]. Muitos resultados teóricos estão presentes na literatura de SLSM, dentre os quais destacamos [12], [13], [14], [16], [17], [18], [22], [28], [30], [35] e [41]. Alguns aspectos interessantes sobre como SLSM generalizam SLD podem ser encontrados em [8] e [24].…”

Section: Os Slsmsunclassified

Estabilidade do filtro de kalman para sistemas lineares com saltos markovianos

Gomes

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"A fé não consiste em saber qualé o mistério do universo, mas sim em ter a convicção de que existe um mistério e eleé maior do que nós". Rabino David Wolpe AgradecimentosTentarei expressar em poucas linhas minha gratidãoàs pessoas que de alguma forma estiveram presentes e que muito me ajudaram em meu caminho até aqui.A Deus, pela constante e amorosa presença.A minha família, que sempre me deu suporte de forma incondicional em todos os aspectos possíveis durante meus estudos. Aos meus pais, Vicente e Jovina, pela dedicação, pela educação e pelo esforço para comigo e meus irmãos. Agradeço-os ainda pelo exemplo de pessoasíntegras que são. Aos meus irmãos, Carlos, Claudinei, Márcio, Gil, Jonas e Alexandre, eàs minhas irmãs, Roseli e Eliane, a quem devo tudo que sou.Ao Prof. Dr. Eduardo Fontoura Costa, pela amizade, competência, seriedade e pela forma generosa com que compartilhou seus conhecimentos nestes dois anos de trabalho.Aos professores Ivo Machado da Costa e José Ruidival dos Santos Filho, pelos valorosos ensinamentos no curso de graduação.A CAPES -Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, pelo suporte financeiro.A todos os professores e funcionários do Instituto de Ciências Matemáticas e de Computação da Universidade de São Paulo.A todos os amigos e colegas, em especial, a Aline, Giseli, Laís e Letrícia.Meus sinceros agradecimentos. ResumoO filtro de Kalmané amplamente conhecido e utilizado em aplicações, em virtude de apresentar diversas propriedades interessantes. Este trabalho aborda uma das características mais importantes, a estabilidade do filtro de Kalman aplicado a sistemas lineares discretos com saltos Markovianos. Sistemas desta classe são muito empregados em problemas práticos.Neste trabalho mostramos que o conceito de controlabilidade fraca e detetabilidade estocástica são condições suficientes para estabilidade do filtro de Kalman com relação a condição inicial. No que se refere a estabilidade no sentido mais usual, apresentamos resultados parciais, dependentes de uma condição adicional sobre a cadeia de Markov, bem como uma conjectura.O estudo da estabilidade do filtro de Kalmané relevante, pois filtros instáveis oferecem estimativas de baixa qualidade. O tema tem interesse teórico inerente eé bastante relevante para aplicacões. AbstractKalman filters present several interesting features that make them relevant for many applications. In this work we study one of the main issues in Kalman filtering -stability. We deal with Kalman filters for Markov jump linear systems, a class of systems with applications in many different areas.We consider the concepts of weak controllability and stochastic detectability and we show that they ensure stability of the Kalman filter with respect to the initial condition. As for the stability, we present some results relying in a conjecture and an additional condition on the Markov chain.The study of the stability of the Kalman filter is important, since unstable filters may lead to poor estimates. The stability issue has inherent theoretical int...

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Finite-time stability of discrete-time nonlinear systems: analysis and design

Abstract: Finite-time stability of nonlinear discrete-time systems is studied. Some new analysis results are developed and applied to controller design.

Cited by 26 publications

References 18 publications

A finite-time stability concept and conditions for finite-time and exponential stability of controlled nonlinear systems

A finite-time stability concept and conditions for finite-time and exponential stability of controlled nonlinear systems

Finite-time stability and stabilization of nonlinear stochastic hybrid systems

Estabilidade do filtro de kalman para sistemas lineares com saltos markovianos

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