Exponential Stability of Singularly Perturbed Systems with Time Delay

Liu, Xinzhi; Shen, Xuemin; Zhang, Yi

doi:10.1080/0003681031000063775

Cited by 24 publications

(24 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By the result of [24], system (39) is ε-uniformly exponentially stable for ε ∈ (0, 3]. However, applying (i) of Theorem 6 to system (39), we verify that by setting P 12 = 0, LMI (30) for ε = 0 is feasible.…”

Section: Examplementioning

confidence: 71%

“…The exponential stability of system (39) has been considered in [24]. By the result of [24], system (39) is ε-uniformly exponentially stable for ε ∈ (0, 3].…”

Section: Examplementioning

confidence: 99%

“…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: 98%

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

View full text Add to dashboard Cite

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.

show abstract

Section: Examplementioning

confidence: 71%

“…The exponential stability of system (39) has been considered in [24]. By the result of [24], system (39) is ε-uniformly exponentially stable for ε ∈ (0, 3].…”

Section: Examplementioning

confidence: 99%

mentioning

confidence: 98%

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

View full text Add to dashboard Cite

show abstract

“…Such processes appear commonly in various fields ranging from physical and chemical systems to systems biology, see for instance, [1], [6], [12], [15] and references therein. Due to their wide applications, stability analysis for such systems has received much attention in a context of control theory, starting with the early work [5], see also [4].…”

Section: Introductionmentioning

confidence: 99%

“…Some more recent results were obtained in [1], [12], [15], [16] to deal with complex structures due to disturbances, unknown parameters, multi-stability, and modular behavior. However, much of the past work was on systems not affected by time delays, and most work for systems with time delays either focused on linear systems, or was based on linear approaches such as linearizations and exponential stability, see, for instance [6], [7]. For singularly perturbed linear functional-differential systems, a spectrum analysis approach was used to study exponential stability in [2].…”

Section: Introductionmentioning

confidence: 99%

Robust stability of singularly perturbed systems with delays

Yang

Wang

2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

Abstract-We consider in this work stability of singularly perturbed systems with time delays. It is shown that if the boundary layer system is robustly globally asymptotically stable and if the reduced slow system admits a Lyapunov-Razumikhin function, then the singularly perturbed system has certain "practical and semi-global" asymptotic stability property as the parameter of singular perturbation reduces to zero.

show abstract