For a system having transfer function $$G\left( s \right) = {{ - s + 1} \over {s + 1}},$$ a unit step input is applied at time $$t=0.$$ The value of the response of the system at $$t=1.5$$ sec (round off to three decimal places) is __________.

Let a causal $$LTI$$ system be characterized by the following differential equation, with initial rest condition
$${{{d^2}y} \over {d{t^2}}} + 7{{dy} \over {dt}} + 10y\left( t \right) = 4x\left( t \right) + 5{{dx\left( t \right)} \over {dt}}\,\,$$

Where, $$x(t)$$ and $$y(t)$$ are the input and output respectively. The impulse response of the system is ($$u(t)$$ is the unit step function)

In the system whose signal flow graph is shown in the figure, $${{U_1}\left( s \right)}$$ and $${{U_2}\left( s \right)}$$ are inputs. The transfer function $${{Y\left( s \right)} \over {{U_1}\left( s \right)}}\,$$ is

A closed loop system has the characteristic equation given by
$${s^3} + K{s^2} + \left( {K + 2} \right)s + 3 = 0.$$ For this system to be stable, which one of the following conditions should be satisfied?