Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems

Zhu, Shuqian; Zhang, Chenghui; Cheng, Zihao; Feng, Jun‐e

doi:10.1109/tac.2007.895951

Cited by 167 publications

(107 citation statements)

References 11 publications

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“…When J 01 = J 11 = 0, the stability of the deterministic singular system (20) with u(t) = 0 has been studied in [31,34,35]. In the following, we will show that LMIs (11) for ε = 0 guarantee mean square exponential stability of the stochastic singular system (20).…”

Section: Proposition 1 If There Exists a Scalar Such That (mentioning

confidence: 99%

“…In [34,35], delay-dependent stability for deterministic singular system with constant delay was studied by using a free-weighting matrix technique. Recently, in [31], this technique was applied to obtain delaydependent stability conditions for deterministic singular system with multiple variable delays.…”

Section: Remarkmentioning

confidence: 99%

“…For any constant delay satisfying 0 h, the deterministic singular time-delay system (24) is exponentially stable, if there exist n ×n matrix P 0 of the form (22), n ×n matrices Q 0, Z > 0, Y , W , such that the following LMI holds: [34,35].…”

Section: Corollarymentioning

confidence: 99%

See 2 more Smart Citations

Exponential stability and exponential stabilization of singularly perturbed stochastic systems with time-varying delay

Chen

Yang

Lü

et al. 2010

Int. J. Robust Nonlinear Control

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SUMMARYIn this paper, the problems of exponential stability and exponential stabilization for linear singularly perturbed stochastic systems with time-varying delay are investigated. First, an appropriate Lyapunov functional is introduced to establish an improved delay-dependent stability criterion. By applying free-weighting matrix technique and by equivalently eliminating time-varying delay through the idea of convex combination, a less conservative sufficient condition for exponential stability in mean square is obtained in terms of ε-dependent linear matrix inequalities (LMIs). It is shown that if this set of LMIs for ε = 0 are feasible then the system is exponentially stable in mean square for sufficiently small ε 0. Furthermore, it is shown that if a certain matrix variable in this set of LMIs is chosen to be a special form and the resulting LMIs are feasible for ε = 0, then the system is ε-uniformly exponentially stable for all sufficiently small ε 0. Based on the stability criteria, an ε-independent state-feedback controller that stabilizes the system for sufficiently small ε 0 is derived. Finally, numerical examples are presented, which show our results are effective and useful.

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Section: Proposition 1 If There Exists a Scalar Such That (mentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Exponential stability and exponential stabilization of singularly perturbed stochastic systems with time-varying delay

Chen

Yang

Lü

et al. 2010

Int. J. Robust Nonlinear Control

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show abstract

“…Table 2 gives the comparison of the maximum allowed delayh for various values of the parameter α. It is clear that the conditions in this paper give better results than those in [14,16,33,36], showing the advantage of the stability result in this paper.…”

Section: Numerical Examplesmentioning

confidence: 72%

Delay Dependent Robust Stability of Singular Systems with Additive Time-varying Delays

Chaibi¹,

Tissir²,

Hmamed³

2013

Int. J. Autom. Comput.

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This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive timevarying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

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“…The robust stability and robust stabilization of uncertain singular systems with single state delay are considered in [8]. The delaydependent robust stability criteria for two classes of singular time-delay systems with norm-bounded uncertainties are proposed in [11], which ensure that the systems are regular, impulse free and asymptotically stable for all admissible uncertainties. A great num-ber of results based on the theory of regular systems have been extended to the area of singular systems [9,10].…”

Section: Introductionmentioning

confidence: 99%

Robust Stability for a Class of Uncertain Singular Time-Delays Systems

Li¹,

Dong²,

Liu³

et al. 2010

IJIES

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This note provides new stability criteria for a class of uncertain singular systems with multiple-state delays. By introducing the state transformation, the study of the robust stability for original systems is changed into this study for the equivalent systems. Based on the Lyapunov-Krasovskii functional combination with LMI techniques, a delay-dependent robust stability criterion for the nominal systems of a class of uncertain singular systems is established, which ensures the nominal systems are asymptotically stable. Furthermore, the delay-dependent robust stability criterion for a class of uncertain singular systems with multiple-state delays is presented, which ensures the class of uncertain singular systems is asymptotically stable. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

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Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems

Cited by 167 publications

References 11 publications

Exponential stability and exponential stabilization of singularly perturbed stochastic systems with time-varying delay

Exponential stability and exponential stabilization of singularly perturbed stochastic systems with time-varying delay

Delay Dependent Robust Stability of Singular Systems with Additive Time-varying Delays

Robust Stability for a Class of Uncertain Singular Time-Delays Systems

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