Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method

The paper investigates the exponential stability of a linear system of difference equations with variable delays , , where , is a constant square matrix, are square matrices, , and for an . New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed.

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