Controllability and Observerability of Linear Continuous-Time Systems

In this research, we investigate a problem of controllable and observerable for linear Continuous-time systems. We have founded controllable and observerable conditions for the linear continuous-time system. Moreover, we put out a new algorithm for finding control vector of steps that can enable us to move the state vector from the initial stage x(0) into the final onex(tf) for finite time tf>0, the theoretical results is illustrated by an example. Finally,we put program to plot trajectory of state vector x(t) and observer vector y(t)