On stability of time-inhomogeneous Markov jump linear systems

Lun, Yuriy Zacchia; D’Innocenzo, Alessandro; Benedetto, Maria Domenica Di

doi:10.1109/cdc.2016.7799118

Cited by 11 publications

(7 citation statements)

References 32 publications

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“…The next propositions summarize this fact. Proposition 1: [17], [20] For all k ≥ 0, stochastic states v and W, defined by ( 5) and ( 6), respectively, have linear dynamics described by…”

Section: Markov Jump Linear System Modelmentioning

confidence: 99%

“…Remark 1: Results in this section aim at representing some moment dynamics of (3) as deterministic linear systems, a common procedure in MJLS literature [17], [15], [21], [20]. Such description is amenable to several notions of stochastic stability, and sets the stage for the main contributions of this paper, presented in the next two sections.…”

Section: Markov Jump Linear System Modelmentioning

confidence: 99%

“…with Y k0,k given by (20). Then, the switching system (3) is FTSS with respect to (α, β, k 0 , k f , λ, • ).…”

Section: Finite-time Stability Of Switching Networkmentioning

confidence: 99%

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Finite-time behavior of switching networks

Cavalcanti

Balakrishnan

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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This paper addresses the analysis of networked systems with switching topologies modeled by Positive Markov Jump Linear Systems, focusing on finite-time stability criteria. Main results are sufficient conditions to assess finite-time stability, and establish probabilistic bounds on state amplification. In addition, connections between notions of asymptotic and finitetime stability are explored. Numerical examples illustrate how the proposed criteria can help to gain insight on air traffic delay propagation, one of many real world networked systems that are amenable to the analysis herein.

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“…The next propositions summarize this fact. Proposition 1: [17], [20] For all k ≥ 0, stochastic states v and W, defined by ( 5) and ( 6), respectively, have linear dynamics described by…”

Section: Markov Jump Linear System Modelmentioning

confidence: 99%

Section: Markov Jump Linear System Modelmentioning

confidence: 99%

See 1 more Smart Citation

Finite-time behavior of switching networks

Cavalcanti

Balakrishnan

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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“…We have not explicitly considered more general policies, because providing an efficient test for certifying the stability of the EHCS under general transmission policies is technically challenging. In particular, recent results from the MJLS literature [21] show that determining the mean-square stability of a MJLS under a time-varying mode transition process is N P-hard. As this is the problem which would be faced if we allowed for time-varying transmission policies, stability certification would be hard for such a problem.…”

Section: Stability Certification For Energy Harvesting Control Systemsmentioning

confidence: 99%

Stability of Control Systems with Feedback from Energy Harvesting Sensors

Watkins¹,

Gatsis²,

Nowzari³

et al. 2017

Preprint

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In this paper, we study the problem of certifying the stability of a closed loop system which receives feedback from an energy harvesting sensor. This is important, as energy harvesting sensors are recharged stochastically, and may only be able to provide feedback intermittently. Thus, stabilizing plants with feedback provided by energy harvesting sensors is challenging in that the feedback signal is only available stochastically, complicating the analysis of the closed-loop system. As the main contribution of the paper, we show that for a broad class of energy harvesting processes and transmission policies, the plant state process can be modeled as a Markov jump linear system (MJLS), which thereby enables a rigorous stability analysis. We discuss the types of transmission policies and energy harvesting processes which can be accommodated in detail, demonstrating the generality of the results.

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“…Nas pesquisas relacionadas aos SLSMs de tempo discreto, as incertezas da MT são, predominantemente, modeladas por politopos, como em Costa et al (1997), Souza (2005) e Lun et al (2016). Neste modelo, as probabilidades de transição pertencem a um conjunto convexo formado pela combinação de matrizes de transição que são os vértices deste conjunto.…”

Section: Introductionunclassified

Reguladores robustos recursivos para sistemas lineares sujeitos a saltos Markovianos com matrizes de transição incertas

Bortolin¹

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Esta tese aborda o problema de regulação para sistemas lineares sujeitos a saltos Markovianos de tempo discreto com matrizes de transição incertas. Considera-se que as incertezas são limitadas em norma e os estados da cadeia de Markov podem não ser completamente observados pelo controlador. No cenário com observação completa dos estados, a solução é deduzida com base em um funcional quadrático dado em termos das probabilidades de transição incertas. Enquanto que no cenário sem observação, a solução é obtida por meio da reformulação do sistema Markoviano como um sistema determinístico, independente da cadeia de Markov. Três modelos são propostos para essa reformulação: um modelo é baseado no primeiro momento do sistema Markoviano, o segundo é obtido a partir da medida de Dirac e resulta em um sistema aumentado, e o terceiro fornece um sistema aumentado singular. Os reguladores recursivos robustos são projetados a partir de critérios de custo quadrático, dados em termos de problemas de otimização restritos. A solução é derivada da técnica de mínimos quadrados regularizados robustos e apresentada em uma estrutura matricial. A recursividade é estabelecida por equações de Riccati, que se assemelham às soluções dos reguladores clássicos, para essa classe de sistemas, quando não estão sujeitos a incertezas. Palavras-chave: Sistemas lineares sujeitos a saltos Markovianos. Probabilidades de transição incertas. Controle robusto. Realimentação de estado. Equação de Riccati.

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On stability of time-inhomogeneous Markov jump linear systems

Cited by 11 publications

References 32 publications

Finite-time behavior of switching networks

Finite-time behavior of switching networks

Stability of Control Systems with Feedback from Energy Harvesting Sensors

Reguladores robustos recursivos para sistemas lineares sujeitos a saltos Markovianos com matrizes de transição incertas

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