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Solution of a Weakly Delayed Difference System
Šafařík, Jan
The paper solves a weakly delayed difference systém x(k+1) = Ax(k)+Bx(k-1) where k = 0;1; : : : , A = (ai j)3 i; j=1, B = (bi j)3i ; j=1 are constant matrices. An explicit solution is given with a discussion on the number of independent initial data.
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Weakly Delayed Systems In ℝ3
Šafařík, Jan
The paper is concerned with a linear discrete system with delay x(k+1) = Ax(k)+Bx(k-m); k = 0,1,…, in R3. It is assumed that the system is weakly delayed. For one of the possible Jordan forms solution of an arbitrary initial problem is given.
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Solution of a Weakly Delayed Difference System
Šafařík, Jan
The paper solves a weakly delayed difference systém x(k+1) = Ax(k)+Bx(k-1) where k = 0;1; : : : , A = (ai j)3 i; j=1, B = (bi j)3i ; j=1 are constant matrices. An explicit solution is given with a discussion on the number of independent initial data.
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Weakly delayed planar linear discrete systems and conditional stability
Šafařík, J.
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.
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