59 views

0 votes

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

- $\dfrac{\mathrm{d^{3}y} }{\mathrm{d^{3}} t}+a_{1}\dfrac{\mathrm{d^{2}y} }{\mathrm{d} t^{2}}+a_{2}\dfrac{\mathrm{d} y}{\mathrm{d} t}+a_{3}y=b_{3}u+b_{2}\dfrac{\mathrm{d} u}{\mathrm{d} t}+b_{1}\dfrac{\mathrm{d^{2}}u }{\mathrm{d} t^{2}}$ (with initial rest conditions)
- $y\left ( t \right )=\int ^{t}_{0}e^{\alpha (t-\tau )}\beta u\left ( \tau \right )d\tau$
- $y=au+b,b\neq 0$
- $y=au$