Weakly delayed planar linear discrete systems and conditional stability

Abstract

A discrete planar system x(k+1) = Ax(k)+B1x(k−m1)+B2x(k−m2), k ≥ 0 is analysed, where m1, m2 are constant integer delays, 0 < m1 < m2, A,B1,B2 are constant 2 × 2 matrices, A = (aij), Bl = (blij), i, j = 1,2, l = 1,2 and x: {−m2,−m2 +1,...} → R2. We get new results on conditional stability and asymptotic conditional stabilit.