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Linear autonomous time-delay system with permutation matrices solving. (English) Zbl 1064.34042

The authors study the existence of solutions of the inhomogeneous delay equation \[ x'(t)=Ax(t)+Bx(t-\tau)+f(t),\quad t\geq 0,\;x(t)=\varphi (t),\;-\tau\leq t\leq 0. \] Assuming that the matrices \(A\) and \(B\) commute, they can write the solutions of this equation in terms of the so-called delayed exponential, the solution of the differential equation with pure delay \[ x'(t)=Bx(t-\tau),\quad t \geq 0,\;x(t)=\varphi(t),\quad -\tau\leq t\leq 0, \] studied before by the authors.

MSC:

34K06 Linear functional-differential equations
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