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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