4. Stationary linear systems

4.1 Matrix exponential

We now recall some useful formulas for linear systems:

\frac{d}{d t} x = A x

with :

The time-dependent matrix exp (tA) is defined by the absolutely convergent series :

exp (t A) = [I + t A + \frac{t^{2}}{2!} A^{2} + \dots + \frac{t^{k}}{k!} A^{k} + \dots]

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(1) - ABRAHAM (R.H.), SHAW (C.D.) - Dynamics – The Geometry of Behavior : I-IV. - Aerial Press, Santa Cruz, California (1981).
(2) - ABRAMOWITZ (M.), STEGUN (I.A.) - Handbook of Mathematical Functions. - Dover, New...

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