Q$1$ Explain about Routh$-$Hurwitz $($RH$)$ criterion for stability analysis of closed loop system. What are necessary and sufficient conditions involved in it$?$ Using RH criterion, comment on the stability of the following systems whose characteristic equation is given by:

$S^4+4S^3+S^2+2S+3=0$

$S^3+2S^2+(K-1)S+K=0($Determine the range of K for which system becomes stable.$)$