On stability of integral delay systems

Melchor-Aguilar, Daniel

doi:10.1016/j.amc.2010.08.058

Cited by 36 publications

(27 citation statements)

References 9 publications

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“…The relationships among these different sufficient conditions are also revealed. Our results improve those in [16]. Both theoretical analysis and numerical examples will demonstrate that the obtained results are always less conservative and more efficient than the existing ones especially those in [16].…”

Section: Problem Formulation and Preliminariessupporting

confidence: 63%

“…The IDS (1) arises when some transformations are made on differential-difference systems [16]. In this note we are concerned with the stability analysis of the IDS (1).…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Lemma 1 [16] The IDS (1) is exponentially stable if there exists a differentiable functional V : C n,τ → R and three positive constants α i , i = 1, 2, 3, such that…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…This class of IDSs with multiple time delays have been investigated in [16] with the help of the well-known discrete-time and continuous-time Jensen inequalities. In this note, by recognizing that the jointed usage of the conventional discrete-time and continuous-time Jensen inequalities requires that all the integration terms 0 −τi x T (t + s) A T i QA i x (t + s) ds share the same weighting matrix Q, we first establish a so-called multiple Jensen inequality, by which as well as some novel Lyapunov functionals and a new linearization technique, every individual integration term possesses a different weighting matrix, which can introduce more weighting matrices that will be optimized to reduce the conservatism of the corresponding sufficient stability conditions.…”

Section: Introductionmentioning

confidence: 99%

“…This class of IDSs have received renewed interest in recent years. A general stability theorem was build in [15] and was later applied on different forms of IDSs (see [13], [16], [18], and the references therein). In the paper [4] stability conditions are derived for IDS with matrix discrete-continuous measures.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability Analysis of Integral Delay Systems With Multiple Delays

Zhou

2016

IEEE Trans. Automat. Contr.

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This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.

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Section: Problem Formulation and Preliminariessupporting

confidence: 63%

“…The IDS (1) arises when some transformations are made on differential-difference systems [16]. In this note we are concerned with the stability analysis of the IDS (1).…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Lemma 1 [16] The IDS (1) is exponentially stable if there exists a differentiable functional V : C n,τ → R and three positive constants α i , i = 1, 2, 3, such that…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%