Finite-time stability for a linear discrete-time delay systems by using discrete convolution: An LMI approach

Stojanović, Sreten B.; Debeljković, Dragutin Lj.; Mišić, Milan

doi:10.1007/s12555-014-0447-z

Cited by 15 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The formulation of the matrix equation was done in a way that is able to perform the calculation using its factorization form. These results present a natural extension of the contributions presented in [7][8][9][10][11][12].…”

Section: Resultssupporting

confidence: 74%

On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach

Debeljković¹,

Cvetković²,

Buzurović³

et al. 2015

Sci Tech Rev

View full text Add to dashboard Cite

In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1) = A 0 (k) + A 1 x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular and one general solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results.

show abstract

Section: Resultssupporting

confidence: 74%

On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach

Debeljković¹,

Cvetković²,

Buzurović³

et al. 2015

Sci Tech Rev

View full text Add to dashboard Cite

show abstract

“…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

Containment control for directed networks multi-agent system with nonlinear dynamics and communication time-delays

Chen

Liu

et al. 2017

Int. J. Control Autom. Syst.

View full text Add to dashboard Cite

Finite-time stability for a linear discrete-time delay systems by using discrete convolution: An LMI approach

Cited by 15 publications

References 23 publications

On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach

On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach

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

Containment control for directed networks multi-agent system with nonlinear dynamics and communication time-delays

Contact Info

Product

Resources

About