ESE 2021 Technical Quiz || State Space Analysis

Which of the following statements are correct?

1) The pair (AB) is controllable implies that the pair (A^TB^T) is observable.

2) The pair (AB) is controllable implies that the pair (A^TB^T) is unobservable.

3) The pair (AC) is observable implies that the pair (A^TC^T) is controllable.

4. The pair (AC) is observable implies that the pair (A^TC^T) is uncontrollable.

Statement 1: State Space model of a system is unique.

Statement 2: State space model can be derived from transfer function.

The system X(t) = Ax(t) + Bu(t) with

 is:

The state variable description of an LTI system is given by

Where y is output and u is the input. The system is observable for

Consider the system shown below, represented by differential equation.

The state diagram with zero initial conditions is given by