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Original Articles

Robust stability, ℋ2 analysis and stabilisation of discrete-time Markov jump linear systems with uncertain probability matrix

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Pages 470-481 | Received 13 Jun 2007, Accepted 16 Apr 2008, Published online: 23 Feb 2009

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R. O. Lopes, Eduardo M. A. M. Mendes, L. A. B. Torres, A. N. Vargas & R. M. Palhares. (2021) Finite-horizon suboptimal control of Markov jump linear parameter-varying systems. International Journal of Control 94:10, pages 2659-2668.
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Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira & Pedro L. D. Peres. (2017) Reduced-order dynamic output feedback control of uncertain discrete-time Markov jump linear systems. International Journal of Control 90:11, pages 2368-2383.
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Ying Lin & Ting Shi. (2022) Static Output Feedback l 2 – l ∞ Asynchronous Control of Markov Jump Systems Under Dynamic Event-Triggered Scheme . IEEE Access 10, pages 97748-97757.
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Jorge C. Guerrero, Jorge R. Chávez-Fuentes, Juan E. Casavilca & Eduardo F. Costa. (2021) Stability analysis of discrete-time Markov jump linear singular systems with partially known transition probabilities. Systems & Control Letters 158, pages 105057.
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Alessandro N. Vargas, Sérgio M. Filho, Cristiano M. Agulhari, Marcio A. F. Montezuma & Eduardo F. Costa. (2020) Stabilizing nonlinear Markov jump systems with orthogonality between control and nonlinear terms. International Journal of Robust and Nonlinear Control 30:13, pages 5122-5133.
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Nuo Xu & Liankun Sun. (2019) Parallel distributed compensation controller design for Markovian jump system with time-varying delays using Bessel-Legendre inequality method and improved positive definite rule. Transactions of the Institute of Measurement and Control 42:7, pages 1313-1322.
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Dayana C. dos Santos, Marcos G. Todorov & Marcelo D. Fragoso. (2019) Robustness Margins for Continuous-time Markov Jump Linear Systems with Uncertain Transition Rates. Robustness Margins for Continuous-time Markov Jump Linear Systems with Uncertain Transition Rates.
Alessandro N. Vargas, Marcio A.F. Montezuma, Xinghua Liu & Ricardo C.L.F. Oliveira. (2019) Robust stability of Markov jump linear systems through randomized evaluations. Applied Mathematics and Computation 346, pages 287-294.
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Cecilia F. Morais, Jonathan M. Palma, Pedro L. D. Peres & Ricardo C. L. F. Oliveira. (2018) $\mathscr{H}_{2}$ and $\mathscr{H}_{\infty}$ mode-independent state-feedback control of generalized Bernoulli jump systems with uncertain probabilities. $\mathscr{H}_{2}$ and $\mathscr{H}_{\infty}$ mode-independent state-feedback control of generalized Bernoulli jump systems with uncertain probabilities.
Jonathan M. Palma, Ceilia F. Morais & Ricardo C. L. F. Oliveira. (2018) $\mathscr{H}_{\infty}$ state-feedback gain-scheduled control for MJLS with non-homogeneous Markov chains. $\mathscr{H}_{\infty}$ state-feedback gain-scheduled control for MJLS with non-homogeneous Markov chains.
Alessandro N. Vargas, Gisela Pujol & Leonardo Acho. (2017) Stability of Markov jump systems with quadratic terms and its application to RLC circuits. Journal of the Franklin Institute 354:1, pages 332-344.
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Alessandro N. Vargas, Leonardo P. Sampaio, Leonardo Acho, Lixian Zhang & Joao B. R. do Val. (2016) Optimal Control of DC-DC Buck Converter via Linear Systems With Inaccessible Markovian Jumping Modes. IEEE Transactions on Control Systems Technology 24:5, pages 1820-1827.
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Cecilia F. Morais, Marcio F. Braga, Ricardo C. L. F. Oliveira & Pedro L. D. Peres. (2016) An LMI approach for H<inf>2</inf> dynamic output feedback control of discrete-time Markov systems with uncertain probabilities. An LMI approach for H<inf>2</inf> dynamic output feedback control of discrete-time Markov systems with uncertain probabilities.
Cecilia F. Morais, Marcio F. Braga, Ricardo C. L. F. Oliveira & Pedro L. D. Peres. (2016) LMI-based design of ℋ∞ dynamic output feedback controllers for MJLS with uncertain transition probabilities. LMI-based design of ℋ∞ dynamic output feedback controllers for MJLS with uncertain transition probabilities.
Marcos G. Todorov & Marcelo D. Fragoso. (2016) New methods for mode-independent robust control of Markov jump linear systems. Systems & Control Letters 90, pages 38-44.
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Alessandro N. Vargas, Eduardo F. Costa & João B. R. do ValAlessandro N. Vargas, Eduardo F. Costa & João B. R. do Val. 2016. Advances in the Control of Markov Jump Linear Systems with No Mode Observation. Advances in the Control of Markov Jump Linear Systems with No Mode Observation 7 33 .
Alessandro N. Vargas, Eduardo F. Costa & João B. R. do ValAlessandro N. Vargas, Eduardo F. Costa & João B. R. do Val. 2016. Advances in the Control of Markov Jump Linear Systems with No Mode Observation. Advances in the Control of Markov Jump Linear Systems with No Mode Observation 1 5 .
Cecília F. Morais, Márcio F. Braga, Márcio J. Lacerda, Ricardo C. L. F. Oliveira & Pedro L. D. Peres. (2015) ℋ2 and ℋ∞ filter design for polytopic continuous-time Markov jump linear systems with uncertain transition rates. International Journal of Adaptive Control and Signal Processing 29:10, pages 1207-1223.
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Alessandro N. Vargas, Daiane C. Bortolin, Eduardo F. Costa & João B.R. do Val. (2015) Gradient-based optimization techniques for the design of static controllers for Markov jump linear systems with unobservable modes. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 28:3, pages 239-253.
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Cecília F. Morais, Márcio F. Braga, Ricardo C.L.F. Oliveira & Pedro L.D. Peres. (2015) state feedback control for MJLS with uncertain probabilities . Automatica 52, pages 317-321.
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Ding Zhai, Liwei An, Jinghao Li & Qingling Zhang. (2015) Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities. Mathematical Problems in Engineering 2015, pages 1-14.
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Julia Emelianova, Pavel Pakshin, Krzysztof Gałkowski & Eric Rogers. (2015) Stability of nonlinear discrete repetitive processes with Markovian switching. Systems & Control Letters 75, pages 108-116.
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Marcos G. Todorov & Marcelo D. Fragoso. (2014) New methods for mode-independent robust control of Markov jump linear systems. New methods for mode-independent robust control of Markov jump linear systems.
Ricardo C. L. F. Oliveira, Alessandro N. Vargas, Joao B. R. do Val & Pedro L. D. Peres. (2014) Mode-Independent <inline-formula> <tex-math notation="LaTeX">${\cal H}_{2}$ </tex-math> </inline-formula>-Control of a DC Motor Modeled as a Markov Jump Linear System. IEEE Transactions on Control Systems Technology 22:5, pages 1915-1919.
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Yang Song, Hao Dong, Taicheng Yang & Minrui Fei. (2014) Almost sure stability of discrete‐time Markov jump linear systems. IET Control Theory & Applications 8:11, pages 901-906.
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Cecilia F. Morais, Marcio F. Braga, Ricardo C. L. F. Oliveira & Pedro L. D. Peres. (2014) &#x210B;<inf>&#x221E;</inf> static output feedback control of discrete-time Markov jump linear systems with uncertain transition probability matrix. &#x210B;<inf>&#x221E;</inf> static output feedback control of discrete-time Markov jump linear systems with uncertain transition probability matrix.
Cecília F. Morais, Márcio F. Braga, Ricardo C.L.F. Oliveira & Pedro L.D. Peres. (2013) ℋ 2 control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling . IET Control Theory & Applications 7:12, pages 1665-1674.
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Alessandro N. Vargas, Eduardo F. Costa & João B.R. do Val. (2013) On the control of Markov jump linear systems with no mode observation: application to a DC Motor device. International Journal of Robust and Nonlinear Control 23:10, pages 1136-1150.
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Marcio F. Braga, Cecilia F. Morais, Ricardo C. L. F. Oliveira & Pedro L. D. Peres. (2013) Robust stability and stabilization of discrete-time Markov jump linear systems with partly unknown transition probability matrix. Robust stability and stabilization of discrete-time Markov jump linear systems with partly unknown transition probability matrix.
Alessandro N. VargasWalter Furloni & João B.R. do Val. (2013) Second moment constraints and the control problem of Markov jump linear systems. Numerical Linear Algebra with Applications 20:2, pages 357-368.
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Nasibeh Zohrabi, Hamid Reza Momeni & Amir Hossein Abolmasoumi. (2013) Sliding Mode Control of Markovian Jump Systems with Partly Unknown Transition Probabilities. IFAC Proceedings Volumes 46:2, pages 947-952.
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Pavel Pakshin, Julia Emelianova, Krzysztof Galkowski & Eric Rogers. (2012) Iterative learning control under parameter uncertainty and failures. Iterative learning control under parameter uncertainty and failures.
P. V. Pakshin, K. Gałkowski & E. Rogers. (2011) Linear-quadratic parametrization of stabilizing controls in discrete-time 2D systems. Automation and Remote Control 72:11, pages 2364-2378.
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Carlos A. Silva, Daiane C. Bortolin & Eduardo F. Costa. (2011) An algorithm for the long run average cost problem for linear systems with indirect observation of Markov jump parameters. IFAC Proceedings Volumes 44:1, pages 12668-12673.
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Pavel Pakshin, Krzysztof Galkowski & Eric Rogers. (2011) Robust Stabilization of Repetitive Processes with Possible Failures⋆. IFAC Proceedings Volumes 44:1, pages 2344-2349.
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