Author： DaCunha Jeffrey J.
Publisher： Taylor & Francis Ltd
ISSN： 1023-6198
Source： Journal of Difference Equations and Applications, Vol.11, Iss.15, 2005-12, pp. : 1245-1264
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Abstract
We give a closed form for the unique solution to the n × n regressive time varying linear dynamic system of the form via use of a newly developed generalized form of the Peano-Baker series. We develop a power series representation for the generalized time scale matrix exponential when the matrix A ( t ) = A is a constant matrix. We also introduce a finite series representation of the matrix exponential using the Laplace transform for time scales, as well as a theorem which allows us to write the matrix exponential as a series of ( n - 1) terms of scalar functions multiplied by powers of the system matrix A .
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