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

Scientific Technical Review

Janković Vladimir¹  Buzurović Ivan²  Debeljković Dragutin³  Cvetković Aleksandar⁴  Mišić Milan⁵ 

[1] Belgrade Waterworks and Sewerage System, Belgrade;Harvard Medical School, Medical Physics and Biophysics Division, Boston, MA, USA;University of Belgrade, Faculty of Mechanical Engineering, Department of Control Engineering, Belgrade;University of Belgrade, Faculty of Mechanical Engineering, Department of Mathematics, Belgrade;University of Pristina, Faculty of Technical Science, Kosovska Mitrovica;

关键词: discrete system;    linear system;    time delay system;    system stability;    finite time stability system;    discrete mathematics;    particular solution;    numerical result;   

DOI  :  

来源: DOAJ

【 摘 要 】

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)=A0(k)+A1x(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.

【 授权许可】

Unknown