Asymptotic practical stability of time delay systems

In this paper, finite-time stability and practical stability problems for a class of linear continuous time-delay systems are studied. Based on the Lyapunov-like functions, that do not have to be positive definite in the whole state space and not need to have negative definite derivatives along the system trajectories, the new sufficient finite-time stability conditions are obtained. To obtain the conditions for attractive practical stability, the mentioned approach is combined with classical Lyapunov technique to guarantee attractivity properties of system behavior, and new delay dependent sufficient condition has been derived. The described approach was compared with some previous methods and it has been showed that the results derived are commonly adequate but easier for numerical treatment.

The article provides sufficient conditions for both practical and finite time stability of linear continuous time delay systems described as

European Journal of Control, 2011

IEEE/CAA Journal of Automatica Sinica, 2019

This paper investigates the stability problem for time-varying delay systems. To obtain a larger delay bound, this paper uses the second-order canonical Bessel-Legendre (B-L) inequality. Secondly, using four couples of integral terms in the augmented Lyapunov-Krasovskii function (LKF) to enhance the relationship between integral functionals and other vectors. Furthermore, unlike the construction of the traditional LKF, a novel augmented LKF is constructed with two new delay-product-type terms, which adds more state information and leads to less conservative results. Finally, two numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed stability criteria.

2013

In the present study, the practical and finite time stability of linear continuous system with latency has been investigated. The proposed result outlines the novel sufficient stability conditions for the systems represented by the following equation: x(t)=A 0 x(t) -A 1 x(t -). The results can be applied to the analysis of both the practical and finite time stability of the continuous systems with time delay. For the derivation of the finite time stability conditions, the Lyapunov-Krassovski functionals were used. Unlike in the previously reported results, the functionals did not have to satisfy some strict mathematical conditions, such as positivity in the whole state space and possession of the negative derivatives along the system state trajectories. The numerical examples presented in this study additionally clarified the implementation of the methodology, and the calculations of the stability conditions. Generally, it was found that the proposed sufficient conditions were less restrictive compared to the ones previously reported.

IEEE/CAA Journal of Automatica Sinica, 2020

In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities (LMIs) to study the global asymptotic stability of state-delay systems. Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a pH neutralizing process are provided to demonstrate the efficacy of the proposed method.

2007 46th IEEE Conference on Decision and Control, 2007

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay dependent stability conditions are then formulated in terms of linear matrix inequalities (LMI). Finally, an example shows the effectiveness of the proposed methodology.

In this paper, a procedure for construction of quadratic Lyapunov–Krasovskii functionals for linear time-delay systems is proposed. It is shown that these functionals admit a quadratic low bound. The functionals are used to derive robust stability conditions.

Journal of the Franklin Institute, 2013

This paper considers the problem of time delay-dependent exponential stability criteria for the time-delay linear system. Utilizing the linear inequality matrices (LMIs) and slack matrices, a novel criterion based on the Lyapunov-Krasovskii methodology is derived for the exponential stability of the time-delay system. Based on the criteria condition we concluded that the upper bound of the exponential decay rate for the time-delay system can be easily calculated. In addition, an improved sufficient condition for the robust exponential stability of uncertain time-delay system is also proposed. Numerical examples are provided to show the effectiveness of our results. Comparisons between the results derived by our criteria and the one given in Liu (2004) [1], Mondie and Kharitonov (2005) [2], and Xu et al. (2006) [3] show that our methods are less conservative in general. Furthermore, numerical results also show that our criteria can guarantee larger exponential decay rates than the ones derived by Liu (2004) [1] and Mondie and Kharitonov (2005) [2] in all time delay points we have tested and in some of time delay points obtained by Xu et al. (2006) [3].

IET Control Theory & Applications, 2010

This study is concerned with the stability analysis of systems with time-varying delay in a given interval. A new type of augmented Lyapunov functional which contains some triple-integral terms is proposed. By introducing free-weighting matrices, a new delay-range-dependent stability criterion is derived in terms of linear matrix inequality. The rate-range of the delay is considered, so the stability criterion is also delay-raterange dependent. Numerical examples are given to illustrate the effectiveness of the proposed method.