Novel conditions for finite time stability of discrete time delay systems

Debeljković, Dragutin Lj.; Buzurović, Ivan; Stojanović, Sreten B.; Jovanovic, Aleksandra M.

doi:10.1109/icsse.2013.6614655

Cited by 3 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The finite-time stability (FTS) approach was introduced by Dorato in [43]. A very few FTS problems have been studied for discrete-time cases in the literature [44][45][46][47]. In addition, Mathiyalagan et al [48] examined the robust finite-time passivity (FTP) problem of DNNs with time delay by using the concept of finite-time boundedness.…”

Section: Introductionmentioning

confidence: 99%

Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

et al. 2021

View full text Add to dashboard Cite

In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology.

show abstract

Section: Introductionmentioning

confidence: 99%

Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Table 1 using various methods: [17], [18], [21] From Table 1, it follows that Theorem 1 gives significantly better results than [17] and [18], but slightly poor results than [21] and [22]. However, unlike [21] and [22], which use LMI, Theorem 1 is based on algebraic inequalities, which can be solved without using appropriate optimization methods.…”

Section: T R R T R T T T R T T T X T Q X T D Q Q Q X T X T E E D X T mentioning

confidence: 99%

“…Similar to the non-delay systems, we can define FTS for time-delay systems. In references [12][13][14][15][16][17][18], some basic results on FTS are derived. These results are conservative, because they use the inequalities based on the norm of state vector.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Stability of Continuous Time Delay Systems: Lyapunov-like Approach with Jensen’s and Coppel’s Inequality

2013

APH

View full text Add to dashboard Cite

show abstract

Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities

Saravanakumar

Stojanović

Radosavljevic

et al. 2019

IEEE Trans. Neural Netw. Learning Syst.

View full text Add to dashboard Cite

In this paper, we study the problem of finite-time stability and passivity criteria for discrete-time neural networks (DNNs) with variable delays. The main objective is how to effectively evaluate the finite-time passivity conditions for NNs. To achieve this, some new weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of a novel Lyapunov-Krasovskii functional, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed results.

show abstract

Novel conditions for finite time stability of discrete time delay systems

Cited by 3 publications

References 10 publications

Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

Finite-Time Stability of Continuous Time Delay Systems: Lyapunov-like Approach with Jensen’s and Coppel’s Inequality

Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities

Contact Info

Product

Resources

About