A unity feedback control system is characterized by the open loop transfer function $$G(s) = {{10k\left( {s + 2} \right)} \over {\left( {{s^3} + 3{s^2} + 10} \right)}}$$ The Nyquist path and the corresponding Nyquist plot of g(s) are shown in the figures below. If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is

Consider the state space realization $$$\left[ {\matrix{ {\mathop x\limits^ \bullet } & {\left( t \right)} \cr {\mathop x\limits^ \bullet } & {\left( t \right)} \cr } } \right] = \left[ {\matrix{ 0 & 0 \cr 0 & { - 9} \cr } } \right]\left[ {\matrix{ {{x_1}} & {\left( t \right)} \cr {{x_2}} & {\left( t \right)} \cr } } \right] + \left[ {\matrix{ 0 \cr {45} \cr } } \right]u\left( t \right),$$$ with the initial condition $$\left[ {\matrix{ {{x_1}} & {\left( 0 \right)} \cr {{x_2}} & {\left( 0 \right)} \cr } } \right] = \left[ {\matrix{ 0 \cr 0 \cr } } \right];$$
Where u(t) denotes the unit step function.
The value of $$\mathop {Lt}\limits_{x \to \infty } \left| {\sqrt {{x_1}^2\left( t \right) + {x_2}^2\left( t \right)} } \right|$$ is ______

A second order LTI system is described by the following state equation. $$$\eqalign{ & {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0 \cr & {d \over {dt}}{x_2}\left( t \right) + 2{x_1}\left( t \right) + 3{x_2}\left( t \right) = r\left( t \right) \cr} $$$

When x₁(t) and x₂(t) are the two state variables and r(t) denotes the input. The output c(t)=X₁(t). The systyem is

In a DRAM,