Robust stability, ℋ<sub>2</sub> analysis and stabilisation of discrete-time Markov jump linear systems with uncertain probability matrix

Oliveira, Ricardo C. L. F.; Vargas, Alessandro N.; Val, J.B.R. do; Peres, Pedro L. D.

doi:10.1080/00207170802136178

Cited by 40 publications

(51 citation statements)

References 32 publications

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“…At the price of testing a finite set of scalar parameter values inside the interval, less conservative results are obtained in terms of H 2 guaranteed costs when compared with the existing conditions. The proposed conditions can cope with H 2 control of MJLS under complete or partial mode observation (as in NCS where transmission failures can occur), generalising the results in [16,28]. By means of numerical experiments, the better efficiency and less conservatism of the proposed conditions are highlighted when compared with the techniques available in the literature.…”

Section: Introductionmentioning

confidence: 90%

ℋ ₂ control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling

Morais

Braga

Oliveira

et al. 2013

IET Control Theory & Applications

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This study is concerned with the problem of H 2 state-feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the transition probability matrix is not precisely known, but belongs to a polytopic domain, or contains unknown or bounded elements. As a first contribution, the uncertainties of the transition probability matrix are modelled in terms of the Cartesian product of simplexes, called multi-simplex. Thanks to this representation, the problem of robust mean square stability analysis with an H 2 norm bound can be solved through convergent linear matrix inequality (LMI) relaxations constructed in terms of polynomial solutions. The proposed conditions yield a better trade-off between precision and computational effort when compared with other methods. As a second contribution, new conditions in terms of LMIs with a scalar parameter lying in the interval (−1, 1) are proposed for H 2 state-feedback control with complete, partial or no observation of the Markov chain. Owing to the presence of the scalar parameter, less conservative results when compared with other conditions available in the literature can be obtained, at the price of increasing the associated computational effort. Numerical examples illustrate the advantages of the proposed methodology.

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Section: Introductionmentioning

confidence: 90%

ℋ ₂ control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling

Morais

Braga

Oliveira

et al. 2013

IET Control Theory & Applications

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“…has a solution V (x, r), satisfying (8) and (9). Then the discrete nonlinear repetitive process obtained by applying u = ϕ(x, r) to (1) and (16) Proof.…”

Section: Theoremmentioning

confidence: 99%

“…In particular, a process with failures is modeled by a state-space model with jumps in the parameter values and/or structure governed by a Markov chain with a finite set of states, often termed Markovian jump systems or systems with random structure, see, for example, [7]. Results on the development of control theory for Markovian jump systems, which address issues such as stability, optimal and robust control problems, in the standard, or 1D, case can be found in, for example, [8][9][10][11][12][13]. These results cannot be applied to 2D systems.…”

Section: Introductionmentioning

confidence: 99%

Stability of nonlinear discrete repetitive processes with Markovian switching

Emelianova

Pakshin

Gałkowski

et al. 2015

Systems & Control Letters

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a b s t r a c tRepetitive processes are a class of 2D systems that operate over a subset of the upper-right quadrant of the 2D plane. Applications include iterative learning control where experimental verification has been reported based on a linear time-invariant model approximation of the dynamics. This paper considers discrete nonlinear repetitive processes with Markovian switching and applies, as one application, the resulting stability theory to iterative learning control for a class of networked systems where time-varying dynamics arise.

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“…One way of describing failure-prone systems is by state-space models with jumps in the parameter values and/or structure governed by a Markov chain with a finite set of states, often termed Markovian jump systems or systems with random structure, see, e.g., [14][15][16][17]. Relevant results regarding the issues of stability, optimal and robust control problems in the 1D case can be found in, e.g., [18][19][20]. In [21,22] discrete-time 2D Markovian jump systems, viz., the problems of stabilization via state feedback H ∞ control and H ∞ filtering are investigated.…”

Section: Introductionmentioning

confidence: 99%

Linear-quadratic parametrization of stabilizing controls in discrete-time 2D systems

Pakshin¹,

Gałkowski

Rogers

2011

Autom Remote Control

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Abstract-This paper considers a class of linear discrete-time 2D systems in the form of repetitive processes with uncertain parameters. Using LQR theory ideas a parametric description of stabilizing controls via output feedback is developed, which leads to the development of efficient LMI-based algorithms for computation of the gain matrix. The results are extended to repetitive processes with Markovian jumps, and a numerical example is given to demonstrate the application of the algorithm developed to the synthesis of stabilizing control laws.

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

Cited by 40 publications

References 32 publications

ℋ ₂ control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling

ℋ ₂ control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling

Stability of nonlinear discrete repetitive processes with Markovian switching

Linear-quadratic parametrization of stabilizing controls in discrete-time 2D systems

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

Cited by 40 publications

References 32 publications

ℋ 2 control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling

ℋ 2 control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling

Stability of nonlinear discrete repetitive processes with Markovian switching

Linear-quadratic parametrization of stabilizing controls in discrete-time 2D systems

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

ℋ ₂ control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling

ℋ ₂ control of discrete‐time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi‐simplex modelling