The main tools of analysis of single input and single output (SISO) systems are transfer function and frequency response methods where the systems must be linear time invariant. These tools cannot be applied for time varying and non-linear systems. In conventional control theory the main theme is to formulate the transfer function putting all initial conditions to zero. The state variable analysis takes care of initial conditions automatically and it isalso possible to analyze time varying or time-invariant, linear or non-linear, single or multiple input-output systems. The main target of this chapter is to introduce state variable analysis for continuous systems.