1.

Let the input be u and the output is y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

A. \(\frac{d^3y}{dt^3}+a_1\frac{d^2y}{dt^2}+a_2\frac{dy}{dt}+a_3y = b_3u + b_2\frac{du}{dt}+ b_1\frac{d^2u}{dt^2} \) (with initial rest conditions)
B. \(y\left( t \right) = \mathop \smallint \limits_0^t {e^{\alpha \left( {t - \tau } \right)}}\beta u\left( \tau \right)d\tau \)
C. y = au + b, b ≠ 0
D. y = au
Answer» D. y = au


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