Optimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml10" display="inline" overflow="scroll" altimg="si10.gif"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> filtering for singular Markovian jump systems

Park, Chan-eun; Kwon, Nam Kyu; Park, PooGyeon

doi:10.1016/j.sysconle.2018.05.005

Cited by 30 publications

(27 citation statements)

References 19 publications

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“…An asynchronous filter is considered such that the phenomena of asynchronous modes between the original SMJSs and the considered filter is modelled as a hidden Markov model. In [15]- [19], H ∞ filtering has respectively reported for SMJSs, and some sufficient conditions on full-and reduced-order H ∞ filtering have been derived. Especillay, the NS full-order H ∞ filter condition for SMJSs has been achieved in [19].…”

Section: Introductionmentioning

confidence: 99%

“…In [15]- [19], H ∞ filtering has respectively reported for SMJSs, and some sufficient conditions on full-and reduced-order H ∞ filtering have been derived. Especillay, the NS full-order H ∞ filter condition for SMJSs has been achieved in [19]. However, the information of all TRs and estimated state are required.…”

Section: Introductionmentioning

confidence: 99%

“…However, the information of all TRs and estimated state are required. It is hard to extend the condition in [19] to the reduced-order filtering problems for SMJSs with ITRs. Thus, how to derive an NS condition on reduced-order filtering with ITRs constitutes this paper.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the reduced-order H ∞ filtering problem is considered for SMJSs with ITRs. Note that the achieved H ∞ filter matrices in [19] depend on all information of TRs and the estimated state. Thus, its method cannot be extended to the reduced-order ones for SMJSs with ITRs.…”

Section: Introductionmentioning

confidence: 99%

“…The filter matrices can be computed by a set of LMIs. However, similar with [19], the full-order NS conditions cannot be extended to the reduced-order ones due to some special matrix structure (such as Λ i in [19]). In this case, tuning the order of filter matrices and without separating the augmented system matrices (i.e.Ā i ,B wi ), the NS reduced-order H ∞ filtering is proposed for SMJSs with ITRs.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Zhang

2020

IEEE Access

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This paper considers the reduced-order H ∞ filtering problem for singular Markovian jump systems (SMJSs) with incomplete transition rates (ITRs) by using augmented system method. The considered conditions in this paper are necessary and sufficient (NS), whereas the existing conditions are mainly sufficient. To be concrete, by extracting system matrices in the considered system from augmented system, NS condition for the existence of the full-order H ∞ filtering is provided in terms of linear matrix inequalities (LMIs). However, it is hard to extend the condition to the existence of the reduced-order H ∞ filtering. Thus, by fixing augmented system matrices, NS condition for the existence of the reduced-order one is presented to guarantee the desired filtering error system to be stochastically admissible with H ∞ performance level. Furthermore, there are neither complicated matrix transformation nor equality/rank constraints in this paper. One numerical and one practical examples are illustrated to demonstrate the effectiveness of the achieved results. INDEX TERMS Singular Markovian jump system, incomplete transition rates, sufficient and necessary conditions, reduced-order filtering.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Zhang

2020

IEEE Access

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Hidden Markov model‐based asynchronous exponential stabilization for stochastic Markovian jump systems with incomplete controller mode information

Lu,

Li,

Tian

2023

Asian Journal of Control

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In this paper, the exponential stability of a kind of It Markovian jump system is studied. Specifically, the exponential stability is ensured by designing an asynchronous delayed‐feedback controller, whose modes are inconsistent with those of the original system. We have built the necessary new relationship between controller modes and system modes, which can facilitate the stability analysis and also make the famous existing ones special cases of the proposed one. Moreover, practically ubiquitous controller delays, which occur between the sensors and controllers, to the detriment of the system stability, are taken into account, and their maximum values are provided in a theoretic way. In this way, the exponential stability can be well ensured against controller delays. With an eye to practical applications, the transition rates of the considered system and the designed asynchronous controller are assumed to be uncertain, and they can be well dealt with by using a new approach with lower conservatism. Furthermore, a practical example and some comparative examples are given to demonstrate the effectiveness and superiorities of the obtained conclusion.

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A new result on reachable set estimation for time‐varying delay singular systems

Zhao

2020

Intl J Robust & Nonlinear

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SummaryThis paper is concerned with the reachable set estimation (RSE) problem for singular systems with both time‐varying delays and bounded peak disturbances. The objective is to search a bounded set that contains all the system states under zero initial conditions. By utilizing the theory of {1}‐inverse and Wirtinger‐based integral inequality, an improved criterion is established in terms of the linear matrix inequalities (LMIs) to guarantee that the reachable set of time‐varying delay singular system is regular, impulse‐free and bounded by the intersection of ellipsoids. Here, a relaxed Lyapunov‐Krasovskii functional is employed to solve the addressed RSE problem which does not require all the involved symmetric matrices to be positive definite. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed methods.

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Optimal H∞ filtering for singular Markovian jump systems

Cited by 30 publications

References 19 publications

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Hidden Markov model‐based asynchronous exponential stabilization for stochastic Markovian jump systems with incomplete controller mode information

A new result on reachable set estimation for time‐varying delay singular systems

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