Stability of a Delay Difference System
نویسندگان
چکیده
We consider the stability problem for the difference system xn = Axn−1 +Bxn−k, where A, B are real matrixes and the delay k is a positive integer. In the case A=−I , the equation is asymptotically stable if and only if all eigenvalues of the matrix B lie inside a special stability oval in the complex plane. If k is odd, then the oval is in the right half-plane, otherwise, in the left half-plane. If ‖A‖ + ‖B‖ < 1, then the equation is asymptotically stable. We derive explicit sufficient stability conditions for A I and A −I .
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