Representations of a linear system

The linear system of Section is shown in block diagram To determine the responseof the output of the system y(t) to an input u(t) the initial condition of the state x(0) must be taken intoaccount as well as the input. Figure shows this in a representation of the same system in terms ofthe system transfer function as discussed in a later section. Figure (c) shows shows the equivalenceof the state-space and the transfer function representation by considering of the systems constituents.The initial conditions of a linear system do not affect the sysytem stability or the longer term stablesystem response. So, for much analysis and design, systems with zero-initial conditions are generally Considered.