Exponential stability for singularly perturbed systems with state delays

Drăgan, Vasile; Ioniţă, Anca Daniela

doi:10.14232/ejqtde.1999.5.6

Cited by 7 publications

(14 citation statements)

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“…Considering the fact that the physical meaning of ε implies that ε should be viewed as a small and uncertain positive parameter, the notation of ε-uniform asymptotic stability describes the robust stability of singularly perturbed systems with respect to sufficiently small ε >0. On the other hand, in some of the classic stability results for singularly perturbed systems, the obtained stability conditions actually assure ε-uniform asymptotic stability of singularly perturbed systems, see [14][15][16][17][21][22][23][24]. From the above analysis, a question arises naturally:…”

mentioning

confidence: 99%

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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mentioning

confidence: 99%

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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“…For a nonzero ", one may multiply both sides of the second equation in (19.35) by " 1 and then obtains a DODE. Then, by using a stability criterion obtained in [14] and applying [57,Theorem 3.3], a formula of the complex stability radius is obtained without difficulty. However, in practice, this formulation is less useful because the appearance of small " may make the computation of the stability radius ill-posed.…”

Section: Related and Other Resultsmentioning

confidence: 99%

Spectrum-Based Robust Stability Analysis of Linear Delay Differential-Algebraic Equations

Linh

Thuan

2015

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

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This paper presents a survey of results on the spectrum-based robust stability analysis of linear delay ordinary differential equations (DODEs) and linear delay differential-algebraic equations (DDAEs). We focus on the formulation of stability radii for continuous-time delay systems with coefficients subject to structured perturbations. First, we briefly overview important results on the stability radii for linear time-invariant DODEs and an extended result for linear time-varying DODEs. Then, we survey some recent results on the spectrum-based stability and robust stability analysis for general linear time-invariant DDAEs. IntroductionThis paper is concerned with the robust stability of homogeneous linear timeinvariant delay systems of the formwhere E; A; D 2 K n;n , K D R or K D C, and > 0 represents a time-delay. We study initial value problems with an initial function , so that x.t/ D .t/; for Ä t Ä 0: (19.2)

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“…Note thatΓ a is invertible because of the diagonal dominance condition (5). The closed-loop system model (18) and (19) is more realistic and less assumptive than the model in [23].…”

Section: Continuous-time Closed-loop System With Time-delaymentioning

confidence: 99%

“…The paper [5] studies the stability of linear, singularly perturbed systems with state delays. The work shows that if the origins of the reduced and boundary-layer systems are exponentially stable, then the origin of the full singularly perturbed system is also exponentially stable.…”

Section: Introductionmentioning

confidence: 99%

A Lyapunov-Krasovskii stability analysis for game-theoretic based power control in optical links

Stefanovic

Pavel

2010

Telecommun Syst

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We analyze the stability of a game-theoretic based power control algorithm for optical links in the presence of time-delays. The control objective is to achieve optimal optical signal to noise ratio (OSNR) values for the signal channels. The control algorithms regularly adjust the signal powers entering the link based on a game-theoretic model. Each signal power is modeled as a player, whose goal is to maximize its own utility function. The utility function increases with an increasing OSNR value, and hence requires an increasing signal power. The trade-off is that if one player increases its OSNR value, this adversely affects the OSNR values of all of the other players. In addition to the signal powers, a dynamic price parameter is fed back to the power control algorithms. Time-delay is present for both the channel pricing parameter and the OSNR feedbacks in the link. We study the stability of the closed-loop, time-delay system. The work utilizes singular perturbation theory modified to handle Lyapunov-Krasovskii techniques.

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Exponential stability for singularly perturbed systems with state delays

Cited by 7 publications

References 1 publication

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

Spectrum-Based Robust Stability Analysis of Linear Delay Differential-Algebraic Equations

A Lyapunov-Krasovskii stability analysis for game-theoretic based power control in optical links

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