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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This work was supported by the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006) and Science and Technology Program of Guizhou Province ([2017]5788).
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You, Z., Wang, J. & O’Regan, D. Exponential Stability and Relative Controllability of Nonsingular Delay Systems. Bull Braz Math Soc, New Series 50, 457–479 (2019). https://doi.org/10.1007/s00574-018-0110-z
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DOI: https://doi.org/10.1007/s00574-018-0110-z