Necessary and sufficient condition for robust stability of discrete-time descriptor polytopic systems

Gao, Xueshan; Teo, Kok Lay; Duan, Guang Ren; Zhang, X.

doi:10.1049/iet-cta.2010.0145

Cited by 6 publications

(7 citation statements)

References 24 publications

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“…From condition (19), it is concluded that G i is nonsingular. Thus, it is known that condition (19) with representation (21) is equivalent to (27). This completes the proof.…”

Section: Theorem 2 For a Given Constantsupporting

confidence: 59%

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Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

Wang

Gao

Miao

et al. 2018

Asian Journal of Control

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In this paper, the fault detection problem for a class of discrete-time polytopic uncertain systems is studied. Different from the traditional methods dealing with polytopic uncertainties, not only its values but also the probability distributions are considered. First of all, the above process about polytopic uncertainty is described by applying a Markov process. Then, the original system with polytopic uncertainties becomes to be a Markovian jump system (MJS) without any uncertainty. Accordingly, the fault detection problem is transformed to be a similar one but considered for an MJS. Particularly, the fault detection and isolation (FDI) filter is constructed to be mode-dependent and also said to be polytope-dependent. Since more information of uncertainty is considered, it is claimed that the obtained results are less conservative. Finally, a practical example is used to show the effectiveness and superiority of the proposed methods.

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“…From condition (19), it is concluded that G i is nonsingular. Thus, it is known that condition (19) with representation (21) is equivalent to (27). This completes the proof.…”

Section: Theorem 2 For a Given Constantsupporting

confidence: 59%

“…Thus, how to further reduce the conservatism based on similar techniques is also necessary to be studied. On the other hand, it is seen that inequality (27) is an amplified inequality and could bring some conservatism. Based on the CCL methods in [50,51], it is known that the conservatism of inequality (27) could be further reduced.…”

Section: Remarkmentioning

confidence: 99%

Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

Wang

Gao

Miao

et al. 2018

Asian Journal of Control

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show abstract

“…So, singular system models can better shown the structure of practical systems, which results in that much attention has been focused on the research of such systems in the past decades (see [1]- [6] and the references therein). Since the time delay and nonlinearity are a pair of inherent attributes of practical systems, the real structure of many practical systems must be described by nonlinear time-delay models (not linear ones), and hence the research of nonlinear singular time-delay systems has practical significance.…”

Section: Introductionmentioning

confidence: 99%

Admissibility criteria for a class of nonlinear singular systems with an interval time-varying delay

Zhang

Zou

2014

2014 International Conference on Mechatronics and Control (ICMC)

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This paper investigates the admissibility analysis problem for a class of nonlinear singular systems with an interval time-varying delay. A delay-range-dependent and delay-rateindependent admissibility criterion for nonlinear singular timedelay system is first established. Furthermore, it is shown that the admissibility criterion proposed in this paper is more simple and less conservative than one in [Nonlinear Analysis: Real World Appl., 2011, 12: 1152-1162]. Then, a pair of admissibility criteria for linear singular systems with a constant and time-varying delay are given, respectively. All admissibility criteria are given in the form of simple linear matrix inequalities, which can be easily solved by the YALMIP toolbox of MATLAB. Finally, three numerical examples are given to illustrate the effectiveness of the theoretical method.

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“…In [15], stabilisation condition was further obtained in terms of a strict matrix inequality. This strict definite technique was also extended to the parameter-dependent stability analysis of discretetime descriptor polytopic systems [18], the H ∞ control for discrete-time descriptor systems [16,19], the decentralised control for discrete-time descriptor large-scale systems [20] and the control for discrete-time descriptor Markov jump systems [21] and hybrid systems [22]. However, all these strict LMI-based results are for descriptor systems with the matrix E being constant.…”

Section: Introductionmentioning

confidence: 99%

Robust stability and stabilisation of discrete-time descriptor systems with uncertainties in the difference matrix

Mao

2012

IET Control Theory Appl.

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This study considers the problems of robust stability and stabilisation for linear discrete-time descriptor systems with norm-bounded uncertainties in all the system matrices including that in the difference matrix E. Under the assumption that the difference matrix E is rank-invariant for all admissible uncertainties, the robustness analysis problem under consideration falls into two cases: right-singular case and left-singular case. A necessary and sufficient stability condition and a sufficient stability condition are proposed for the first and second case, respectively. By using a state augmentation technique, sufficient stabilisation conditions are obtained for both cases. Furthermore, a necessary and sufficient stabilisation condition is established in the case of a non-singular matrix E. Finally, illustrative examples show that the proposed conditions are effective to design the stabilising controller for uncertain discrete-time descriptor systems with both the singular and non-singular matrixE.

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Necessary and sufficient condition for robust stability of discrete-time descriptor polytopic systems

Cited by 6 publications

References 24 publications

Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

Admissibility criteria for a class of nonlinear singular systems with an interval time-varying delay

Robust stability and stabilisation of discrete-time descriptor systems with uncertainties in the difference matrix

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