Consider a feedback system with the open loop transfer function given by $$G(s)H(s) = {K \over {s\left( {2s + 1} \right)}}.$$ Examine the stability of the closed-loop system using Nyquist stability.

The phase margin (in degrees) of a system having the loop transfer function is $$G(s)H(s) = {{2\sqrt 3 } \over {s(s + 1)}}$$

For the system described by the state equation $$$\mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr {0.5} & 1 & 2 \cr } } \right]x + \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]u.$$$

If the control signal u is given by u=(-0.5-3-5)x+v, then the eigen values of the closed loop system will be

The circuit diagram of a synchronous counter is shown in the figure. Determine the sequence of states of the counter assuming that the initial state is ‘000’. Give your answer in a tabulor form showing the present state Q_A(n), Q_B(n), Q_C(n), J-K inputs ( J_A, K_A, J_B, K_B, J_C, K,) and the next state $${Q_{A\left( {n + 1} \right)}},\,{Q_{B\left( {n + 1} \right)}},{Q_{C\left( {n + 1} \right)}}$$ From the table, determine the modulus of the counter.