This paper is concerned with an nonautonomous perturbed linear dynamical system xk+1 = Axk+Fk(xk). A well known result of Perron states that this system is asymptotically stable if A is stable and that Fk(x)≡f(x)= o(∥x∥). It is clear that this is purely a local result which gives no information about the size of the region of asymptotic stability nor the size of the solutions. In this paper, estimates for the size of the solutions and regions of stability are derived.
|Number of pages||4|
|Journal||Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering|
|State||Published - 1 Mar 2000|