Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

An unforced linear time invariant (LTI) system is represented by $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right].$$$

If the initial conditions are x₁(0)= 1 and x₂(0)=-1, the solution of the state equation is

Consider the state space model of a system, as given below

The system is

The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations

The state transition matrix e^At of the system shown in the figure above is