<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="normal"><mml:mi>∞</mml:mi></mml:mstyle></mml:mrow></mml:msub></mml:math>filtering for descriptor systems with strict LMI conditions

Beidaghi, Sahereh; Jalali, Ahvand; Ali, Khaki Sedigh

doi:10.1016/j.automatica.2017.02.021

Cited by 39 publications

(12 citation statements)

References 19 publications

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“…Then, we have

ϑ^{T} \{{\bar{Y}}_{i}^{T} (A_{i} + A_{d i}) + {(A_{i} + A_{d i})}^{T} {\bar{Y}}_{i} + λ E^{T} {\bar{Y}}_{i} + \sum_{j = 1}^{N} π_{i j} E^{T} {\bar{Y}}_{i}\} ϑ = 0,

which is a contradiction with . Furthermore, by a similar argument in the works of Xu and Lam and Sahereh et al, we can assume that

{\overset{X}{true}}_{i} - {\overset{Y}{true}}_{i}

is nonsingular. Define

\begin{matrix} right {\hat{P}}_{i} = & left [\begin{matrix} X_{i} & Y_{i} - X_{i} \\ Y_{i} - X_{i} & X_{i} - Y_{i} \end{matrix}], \overset{E}{true} = [\begin{matrix} E & 0 \\ 0 & E \end{matrix}], Ŝ = [\begin{matrix} S & 0 \\ 0 & S \end{matrix}], & right \\ right {\hat{U}}_{i} = & left [\begin{matrix} U_{1 i} & U_{2 i} - U_{1 i} \\ U_{2 i} - U_{1 i} & U_{1 i} - U_{2 i} \end{matrix}] \end{matrix}

…”

Section: Resultsmentioning

confidence: 95%

“…Since the similar work has existed in the works of Wu et al 31 and Wang et al 39 for SMJSs with time-varying delays and the complexity of condition (7) to (12) will increase with the partitioning size increasing, we do not use this approach in our work.…”

Section: Exponential Admissibility and  ∞ Performance Analysismentioning

confidence: 99%

“…andC i ; any matrices U 1i and U 2i ; matrices M ki , k = 1, … , m; and scalars i > 0 for i ∈ S such that conditions (7) to (11) and…”

Section: Mode-dependent Reliable Filter Designmentioning

confidence: 99%

“…, and 4v are defined in Theorem 1. Furthermore, when LMIs (7) to (11), (25), and (26) are feasible, the parameters of mode-dependent filter (5) can be obtained by…”

Section: Mode-dependent Reliable Filter Designmentioning

confidence: 99%

“…During the past decades, singular systems, which couple differential equations with algebraic equations, have received considerable attention since they can be well used to model many practical systems like electrical systems, economic systems, mechanics systems, etc. Lots of results on different kinds of singular systems have been published in the literature; see, eg, other works . Among these, much effort has been done for the analysis and synthesis of singular Markovian jump systems (SMJSs); see, eg, other works and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

Liu

Park

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper deals with the problem of exponential H∞ filtering for singular Markovian jump systems with time‐varying delays subject to sensor failures. The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time‐varying delay and sensor failures is mean‐square exponentially admissible with a specified decay rate and simultaneously satisfies an H∞ performance. First, the delay interval is partitioned into m subintervals and a novel mode‐dependent stochastic Lyapunov‐Krasovskii functional is constructed. By using the reciprocally convex inequality in each subinterval, sufficient conditions of exponential H∞ performance analysis are developed for the considered filtering error system. Then, based on these conditions, the existence conditions of the desired reliable filter are derived and the filter parameters are obtained. It should be mentioned that all the results presented here are not only dependent on the time delay but also dependent on the decay rate and the partitioning size. Furthermore, all the conditions are established in terms of strict linear matrix inequalities. Finally, two numerical examples are given to illustrate the less conservatism and effectiveness of the proposed methods.

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“…Then, we have

ϑ^{T} \{{\bar{Y}}_{i}^{T} (A_{i} + A_{d i}) + {(A_{i} + A_{d i})}^{T} {\bar{Y}}_{i} + λ E^{T} {\bar{Y}}_{i} + \sum_{j = 1}^{N} π_{i j} E^{T} {\bar{Y}}_{i}\} ϑ = 0,

which is a contradiction with . Furthermore, by a similar argument in the works of Xu and Lam and Sahereh et al, we can assume that

{\overset{X}{true}}_{i} - {\overset{Y}{true}}_{i}

is nonsingular. Define

\begin{matrix} right {\hat{P}}_{i} = & left [\begin{matrix} X_{i} & Y_{i} - X_{i} \\ Y_{i} - X_{i} & X_{i} - Y_{i} \end{matrix}], \overset{E}{true} = [\begin{matrix} E & 0 \\ 0 & E \end{matrix}], Ŝ = [\begin{matrix} S & 0 \\ 0 & S \end{matrix}], & right \\ right {\hat{U}}_{i} = & left [\begin{matrix} U_{1 i} & U_{2 i} - U_{1 i} \\ U_{2 i} - U_{1 i} & U_{1 i} - U_{2 i} \end{matrix}] \end{matrix}

…”

Section: Resultsmentioning

confidence: 95%

Section: Exponential Admissibility and  ∞ Performance Analysismentioning

confidence: 99%

“…andC i ; any matrices U 1i and U 2i ; matrices M ki , k = 1, … , m; and scalars i > 0 for i ∈ S such that conditions (7) to (11) and…”

Section: Mode-dependent Reliable Filter Designmentioning

confidence: 99%

“…, and 4v are defined in Theorem 1. Furthermore, when LMIs (7) to (11), (25), and (26) are feasible, the parameters of mode-dependent filter (5) can be obtained by…”

Section: Mode-dependent Reliable Filter Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

Liu

Park

et al. 2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

Observer‐based actuator fault estimation and proportional derivative fault tolerant control for continuous‐time singular systems

Zhang

et al. 2019

Optim Control Appl Methods

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Summary This paper focuses on designing fault estimation (FE) and fault tolerant control (FTC) schemes for continuous‐time singular systems affected by actuator fault. A novel observer called the extended proportional integral observer (PIO) is designed so that the estimations of system state and actuator fault can be obtained simultaneously. In contrast with the traditional PIO, better estimation performance can be obtained by using the designed observer. Furthermore, with the obtained FE information, a novel proportional derivative–type FTC scheme is given by means of the separation property and the free‐weighting matrix technique, which ensures that the closed‐loop system is normal and stable. All the feasible conditions are formulated in linear matrix inequality (LMI) frameworks. Finally, two examples are simulated to prove the superiority and practicability of the presented scheme.

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Event‐triggered feedback control for delayed singular jump systems based on sampled observer and exponential detector

Zhuang

Xia

et al. 2021

Intl J Robust & Nonlinear

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This paper is intended to investigate the problem of event-triggered H ∞ feedback control for time-varying delays singular jump systems based on sampled observer and exponential detector. By virtue of the designed event-triggered control strategies, the state estimate signals are transmitted to the controller under the networked communication environment and aperiodic sampling scheme. The driving threshold is devised by exponentially decreasing function, which is used to guarantee not only the validity of event-triggered strategy but also the admissibility of the delayed singular jump systems. Neoteric stochastic admissibility, stabilization and H ∞ performance conditions are obtained in terms of linear matrix inequalities. Simulation examples including an oil catalytic cracking process are utilized to illustrate the validity and superiority of the proposed event-triggered feedback control technique.

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H∞filtering for descriptor systems with strict LMI conditions

Cited by 39 publications

References 19 publications

Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

Observer‐based actuator fault estimation and proportional derivative fault tolerant control for continuous‐time singular systems

Event‐triggered feedback control for delayed singular jump systems based on sampled observer and exponential detector

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