Robust stability analysis of uncertain systems with two additive time-varying delay components

Wu, Huai‐Ning; Liao, Xiaofeng; Feng, Wei; Guo, Songtao; Zhang, Wei

doi:10.1016/j.apm.2009.03.008

Cited by 61 publications

(57 citation statements)

References 20 publications

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“…The norm-bounded uncertainties can be treated as a special case of nonlinear perturbations [8,14]. Therefore, the criterion obtained in Theorem 1 can be applicable to the system with two additive interval time-varying delays and normbounded uncertainties.…”

Section: Remarkmentioning

confidence: 99%

“…In [12][13], by constructing new Lyapunov functional, some improved delay-dependent stability criteria were derived. In [14], by taking more information of the time-varying delays in Lyapunov functional into account and by utilizing free matrix variables in approximating certain integral terms, a robust stability criterion for uncertain linear systems with two additive time-varying delays was given. In [15], by defining a more general Lyapunov functional and employing convex polyhedron method to estimate the upper bound on the time derivative of the Lyapunov functional, an improved delaydependent stability criterion is established.…”

Section: Introductionmentioning

confidence: 99%

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Delay-Dependent Stability Criteria for Continuous Systems with Two Additive Interval Time-Varying Delays and Nonlinear Perturbations

Jiao¹,

Sun²

2017

IJCA

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Delay-Dependent Stability Criteria for Continuous Systems with Two Additive Interval Time-Varying Delays and Nonlinear Perturbations

Jiao¹,

Sun²

2017

IJCA

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“…The calculation results obtained by Theorem 1 in [4], Theorem 1 in [5], Theorem 1 in [6], Corollary 1 in [7], Theorem 1 in [8], and Corollary 2 in this paper for different cases are listed in Tables 3 and 4. It is clear that Corollary 2 in this paper gives much better results than those obtained by [4−7].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Hence, it is mathematically less complex and computationally more efficient. [7], (N = 1) 11.5n 2 + 4.5n [7], (N = 2) 22.5n 2 + 8.5n [6] 32.5n 2 + 8.5n [8] 15.5n 2 + 3.5n…”

Section: Numerical Examplesmentioning

confidence: 99%

“…An improved stability criterion was proposed by exploiting new Lyapunov-Krasovskii functional [5] . By taking more information of the time-varying delay in Lyapunov-Krasovskii functional into account and by utilizing free matrix variables in approximating certain integral terms, a new robust stability criterion for uncertain linear systems with two additive time-varying components was given [6] . Very recently, by using a delay decomposition method, a delay-dependent absolute stability condition for a class of nonlinear systems with two additive time-varying delay components is presented [7] .…”

Section: Introductionmentioning

confidence: 99%

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A Stability Criterion for Singular Systems with Two Additive Time- varying Delay Components

Jiao

2013

Int. J. Autom. Comput.

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Abstract:The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities (LMIs). Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.

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Improved Stabilization for Continuous Dynamical Systems with Two Additive Time‐Varying Delays

Xiong¹,

Zhou²

2015

Asian Journal of Control

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This paper studies the problem of stabilization criteria for systems with two additive time‐varying delays. First, the delay‐dependent stability condition for the systems is established through computing the more general Lyapunov functional. The Lyapunov functional is constructed by making full use of the property and the information of the systems, and the condition has advantages over the existing ones in the skillful combination of the delay decomposition and the reciprocal convex approach. Second, considered to be more flexible for the controller design with the introduced positive scalar, a new controller method is presented. Finally, two examples are provided to demonstrate the advantage of the results in this paper.

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Robust stability analysis of uncertain systems with two additive time-varying delay components

Cited by 61 publications

References 20 publications

Delay-Dependent Stability Criteria for Continuous Systems with Two Additive Interval Time-Varying Delays and Nonlinear Perturbations

Delay-Dependent Stability Criteria for Continuous Systems with Two Additive Interval Time-Varying Delays and Nonlinear Perturbations

A Stability Criterion for Singular Systems with Two Additive Time- varying Delay Components

Improved Stabilization for Continuous Dynamical Systems with Two Additive Time‐Varying Delays

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