State Space to Transfer Function

State-space representation can also be converted into a transfer function in system analysis.

The transformation begins with the given state and output equations.

The Laplace transform is applied here, assuming zero initial conditions. This transforms the equations from the time domain to the frequency domain.

The state equation is solved for X(s), where I represents the identity matrix. This solution is then substituted into the output equation.

The resulting matrix, known as the transfer function matrix, links the output vector to the input vector.

When these vectors are scalars, it becomes possible to find the final transfer function, thereby completing the transformation from state-space representation to transfer function.

Consider a system defined by matrices of different dimensions that form the state and output equations.

While all other terms in the transfer function equation are already defined, one term remains unknown.

To find this term, the known matrix values are used from the state equation. Further, the inverse is calculated.

Upon substitution, the state-space representation is converted into a transfer function.