Stability bound of multiple time delay singularly perturbed systems

Pan, Shing‐Tai; Hsiao, Feng‐Hsiag; Teng, Ching‐Cheng

doi:10.1049/el:19960644

Cited by 23 publications

(22 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [19,20], stability of deterministic singularly perturbed systems with delays has been studied by frequency domain approach, stability criteria in terms of the H ∞ norm are derived. However, this frequency domain approach is not suitable to stability analysis of singularly perturbed stochastic systems with time-varying delays.…”

Section: Remarkmentioning

confidence: 99%

“…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 the following, we will show that LMIs (11) for ε = 0 guarantee mean square exponential stability of the stochastic singular system (20). To this end, let us introduce stability definition for system (20).…”

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

confidence: 99%

“…In [27], a Lyapunov functional approach was proposed to exploit the stability of singularly perturbed linear time-delay systems with single singular perturbation parameter ε. Different from the frequency domain methods used in [18][19][20]25], the Lyapunov functional approach developed in [27] aims in arriving at stability criteria that can be written in the form of ε-dependent linear matrix inequalities (LMIs). The advantages of this approach lie in two aspects.…”

mentioning

confidence: 99%

See 3 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: Remarkmentioning

confidence: 99%

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

confidence: 99%

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

confidence: 99%

mentioning

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

View full text Add to dashboard Cite

show abstract

“…Also, Shao and Rowland in [7] considered a linear time-invariant singularly perturbed system with single time-delay in the slow states. Then, the research on time-scale modeling was extended to include singularly perturbed systems with multiple time-delays in both slow and fast states [8]. Recently, the problem of robust stabilization and disturbance attenuation for a class of uncertain singularly perturbed systems with norm-bounded nonlinear uncertainties has been considered in [9].…”

Section: Introductionmentioning

confidence: 99%