New results for the stability of uncertain time-delay systems

Lee, Chien-Hua; Li, Tzuu-Hseng S.; Kung, Fan‐Chu

doi:10.1080/00207729508929083

Cited by 3 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Generally speaking, the stability criteria and/or stabilization conditions obtained by Lyapunov methods are su cient but not necessary and include some free parameters (scalars and/or matrices) so that the di erent choices of these free parameters may result in the different results (Xu 1997). Therefore, many researchers have been seeking various methods of choosing the free parameters appropriately to obtain the improved or less conservative results (see, for example, Cheres et al 1989a, Trinh and Aldeen 1995, Chen et al 1995, Lee et al 1995, Wu and Mizukami 1995, Kim 1996, Jeung et al 1996, Xu et al 1996, Luo and van den Bosch 1997, Xu 1997, and the references therein). On the other hand, only asymptotic stability is generally not satis® ed enough in applications, and most satis® ed stability in applications is the stability with some satis® ed decay degrees.…”

Section: Introductionmentioning

confidence: 99%

Decay estimates for retarded dynamic systems

Xu¹

1999

International Journal of Systems Science

View full text Add to dashboard Cite

B ugong X u ² This paper presents some necessary and su cient stability conditions and some sucient stability conditions for general classes of retarded dynam ic systems. The stability conditions are established by using the L yapunov function method. However, attention is paid in this paper to establishing as less conservative exponential, generalized exponential and non-exponential decay estimates for the retarded dynam ic systems as possible. As applications of the established stability conditions, a class of retarded dynam ic systems which have a linear retard-free term are studied in detail and some exponential, generalized exponential and non-exponential iterative decay estimates for the systems are obtained. It is shown that the non-exponential iterative decay estimates are less conservative than the exponential and generalized exponential decay estimates. In addition, the obtained iterative decay estimates involve only algebraic computation; therefore, they are simple and very easy to use. Two examples are given to illustrate the proposed methods and to show the superiority of the obtained results. Remark 2:The de® nition of the decay functions in De® nition 1 depends on the initial instant t 0 J 0 and the di erent t 0 may imply the di erent decay function. (3) and (4) imply that G t and g t only depend on t t 0 for given t 0 , u J 0 C n . The physical meaning of G t is obvious, and as d t, u 1/ g t Ç d t, u , the physical meaning of 1/ g t at t s t 0 can be regarded as the time taken by d t, u from d s, u to 0 when keeping the velocity Ç d s, u . De® nitionsh De® nition 2: The equilibrium x* 0 of system (1) is said to be globally generalized exponentially stable if the solution x t 0 , u t of system (1) through any t 0 , u J 0 C n satis® esThe equilibrium x* 0 of system (1) is said to be globally exponentially stable if the solution x t 0 , u t of system (1) through any t 0 , u J 0 C n satis® esx t 0 , u t G u ¿ exp g t t 0 dt , t t 0 6 where G 1 and g > 0 are constant.h De® nition 4: The equilibrium x* 0 of system (1) is said to be uniformly stable if for e > 0, there is a d d e > 0 such that u ¿ < d implies

show abstract

Section: Introductionmentioning

confidence: 99%

Decay estimates for retarded dynamic systems

Xu¹

1999

International Journal of Systems Science

View full text Add to dashboard Cite

show abstract

A stability criterion for linear uncertain systems with multiple delays

Wang

Da-zhou

ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, 2004.

View full text Add to dashboard Cite

Refined Stability Conditions for Linear Uncertain Systems With Multiple Time-Varying Delays

Huang

2006

Journal of Dynamic Systems, Measurement, and Control

View full text Add to dashboard Cite

This paper mainly proposes distinct criteria for the stability analysis and stabilization of linear uncertain systems with time-varying delays. Based on the Lyapunov theorem, a sufficient condition of the unforced systems with single time-varying delay is first derived. By involving a memoryless state feedback controller, the condition will be extended to treat with the resulting closed-loop system. These explicit criteria can be reformulated in LMIs forms, so we will readily verify the stability or design a stabilizing controller by the current LMI solver. Furthermore, the considered systems with multiple time-varying delays are similarly addressed. Numerical examples are given to demonstrate that the proposed approach is effective and valid.

show abstract

New results for the stability of uncertain time-delay systems

Cited by 3 publications

References 10 publications

Decay estimates for retarded dynamic systems

Decay estimates for retarded dynamic systems

A stability criterion for linear uncertain systems with multiple delays

Refined Stability Conditions for Linear Uncertain Systems With Multiple Time-Varying Delays

Contact Info

Product

Resources

About