Improved stability criteria for linear systems with time-varying delay (original) (raw)
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Improved delay-range-dependent stability criteria for linear systems with time-varying delays
Automatica, 2010
This paper is concerned with the stability analysis of linear systems with time-varying delays in a given range. A new type of augmented Lyapunov functional is proposed which contains some tripleintegral terms. In the proposed Lyapunov functional, the information on the lower bound of the delay is fully exploited. Some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices. Numerical examples are given to illustrate the effectiveness of the proposed method. t t−τ 2 x T (s)Q 2 x(s)ds and t t−d(t) x T (s)Q 3 x(s)ds. The integral upper limit of these terms are all 't'. Therefore, the information on the lower bound of the delay, τ 1 , is not used adequately when the lower bound is 0005-1098/$ -see front matter
Stability Analysis of Systems With Time-varying Delay via a Novel Lyapunov Functional
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.
Delay-dependent stability analysis of linear systems with time-varying delay
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.
New delay-and-delay-derivative-dependent stability criteria for systems with time-varying delay
49th IEEE Conference on Decision and Control (CDC), 2010
This paper provides new delay-and-delayderivative-dependent criteria for systems with the delay and its derivative varying within intervals. With introduction of new Lyapunov-Krasovskii functionals, a less conservative upper bound for the maximum delay is achieved. Examples show that the resulting criteria outperform previously published results in the literature.
Further Stability Criteria for Time-Delay Systems with Interval Time-Varying Delays
Proceedings of the 18th IFAC World Congress, 2011
In this paper, a novel stability criterion is developed for time-delay systems having time-varying delays that belong to a given range. Based on a choice of different type of Lyapunov-Krasovskii functional in an extensively augmented form, some new delay-range dependent stability criteria are proposed. This developed stability result has advantages over some previous ones. First, the method is based on the selection of a new, extensively augmented Lyapunov-Krasovskii functional which does not only take the delay range into account but also the weighted version of it. Second it estimates the upper bound of the derivative of the Lyapunov functional without ignoring some useful integral terms. Finally, we have introduced several free slack variables in relation with Newton-Leibniz formula to provide some kind of relaxation for the proposed stability criteria. In addition to this, we have also employed the method of completing to squares which has enabled to provide further relaxation with some additional decision variables.
International Journal of Dynamics and Control, 2018
This paper studies the problem of delay-range-dependent stability analysis for the continuous-time linear systems with timevarying delay. A new and appropriate Lyapunov-Krasovskii (L-K) functional is constructed. To estimate the quadratic integral terms coming out from the derivative of L-K functional, utilize the well-known Wirtinger integral inequality together with the reciprocal convex lemma. Then, an improved delay-range-dependent stability condition is being established in terms of linear matrix inequalities (LMIs) in such a way that it can be effectively solved by using existing software (LMI toolbox in MATLAB). The delay upper bound results obtained by the developed stability condition are found to be less conservative than other recent results. Furthermore, the proposed stability criterion use the less number of decision variables and give the consistent delay bound results compared to some other methods. Two numerical examples are given to illustrate the effectiveness of the obtained stability condition compared to some recently published stability methods.
Delay-dependent stability analysis for linear system with time-varying delay: a PAM method
A piecewise analysis method (PAM) is proposed to investigate the stability of linear system with timevarying delay and uncertainties. Different from the existing methods in dealing with the time-varying delay, the whole variation interval of the delay is divided into two subintervals with equal length. Respecting for the delay belongs to different subintervals, new criteria on stability analysis of the time delay systems are obtained by checking the variation of the derivative of the Lyapunov functional in the two subintervals. Then, by using the convexity properties of matrix inequality and some other new analysis techniques, new criteria are obtained for the asymptotical stable of the time delay systems. The given numerical examples show that the derived criteria can lead to much less conservative results than those obtained based on the existing methods.
Improved Delay-Dependent Stability for a Class of Linear Systems with Time-Varying Delay and Nonline
Proceedings of the 17th IFAC World Congress, 2008, 2008
This note deals with the robust stability analysis for time-delay systems with nonlinear perturbations. Firstly, a new class of Lyapunov functional candidate is proposed to develop some new criteria by considering the additional useful terms and introducing some freeweighting matrices. Then, an augmented Lyapunov functional is introduced to establish a novel improved stability condition. All results obtained are given in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed methods.
IEEE/CAA Journal of Automatica Sinica, 2021
One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay. The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval. The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer. The second contribution of this paper is to introduce a novel Lyapunov-Krasovskii functional, which includes a cubic polynomial on a time-varying delay, in stability analysis of time-delay systems. Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities, two stability criteria are derived for two cases of the time-varying delay. A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.
Delay-dependent stability criteria for linear systems with multiple time delays
IEE Proceedings - Control Theory and Applications, 2006
This paper deals with the problem of the delay-dependent stability of linear systems with multiple time delays. A new method is first presented for a system with two time delays, in which free weighting matrices are used to express the relationships among the terms of the Leibniz-Newton formula. Next, this method is used to show the equivalence between a system with two identical time delays and a system with a single time delay. Then, a numerical example verifies that the criterion given in this paper is effective and is a significant improvement over existing ones. Finally, the basic idea is extended to a system with multiple time delays.