The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

The unit impulse response of a system is: $$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state value of the output for unit step input is equal to

A linear system is described by the following state equation $$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right) + BU\left( t \right),A = \left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right].$$$
The state-transition matrix of the system is

The transfer function of a phase-lead compensator is given by $${G_c}(s) = {{1 + 3Ts} \over {1 + Ts}}$$

where T > 0. The maximum phase-shift provided by such a compesator is