Stability Results for a Class of Difference Systems with Delay | Zendy

Éva Kaslik | Zendy

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Stability Results for a Class of Difference Systems with Delay

Author(s) -

Éva Kaslik

Publication year - 2009

Publication title -

advances in difference equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.67

H-Index - 51

eISSN - 1687-1847

pISSN - 1687-1839

DOI - 10.1155/2009/938492

Subject(s) - mathematics , class (philosophy) , stability (learning theory) , ordinary differential equation , partial differential equation , delay differential equation , control theory (sociology) , mathematical analysis , differential equation , computer science , artificial intelligence , control (management) , machine learning

Considering the linear delay difference system x(n+1)=ax(n)+Bx(n-k), where a∈(0,1), B is a p×p real matrix, and k is a positive integer, the stability domain of the null solution is completely characterized in terms of the eigenvalues of the matrix B. It is also shown that the stability domain becomes smaller as the delay increases. These results may be successfully applied in the stability analysis of a large class of nonlinear difference systems, including discrete-time Hopfield neural networks

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