Verify by simulation that the time-varying system $$ x = \begin{bmatrix} -2 & -g(t) \\ -3 & x \end{bmatrix} $$ is asymptotically stable for any reasonable $g(t)$ function. Note that numerical overflow may occur on the computer if a $g(t)$ which grows without bound is selected. One suggestion is $g(t) = ae^{bt} \sin(yt)$, with $b \leq 0$.
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The stability analysis of such systems is generally more complex than that of time-invariant systems. Numerical simulation is a suitable approach to verify the stability for a range of $g(t)$ functions. Show more…
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