Abstract
In this paper we consider a delayed matrix exponential and use it to derive a representation of solutions to a linear nonsingular delay problem with permutable matrices. Also we present some sufficient conditions to guarantee that the trivial solution of such delay systems are exponentially stable. In addition using a delay Grammian matrix we present a criterion for a linear problem to be relatively controllable. Nonlinear problems are also discussed. Numerical examples are given to illustrate our theory.
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