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 system expressed by the signal flow diagram shown in the figure.

The corresponding system 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