  In this paper, we tackle the significant challenge of simultaneous
stabilization in control systems engineering, where the aim is to employ a
single controller to ensure stability across multiple systems. We delve into
both scalar and multivariable scenarios. For the scalar case, we present the
necessary and sufficient conditions for a single controller to stabilize
multiple plants and reformulate these conditions to interpolation constraints,
which expand Ghosh's results by allowing derivative constraints. Furthermore,
we implement a methodology based on a Riccati-type matrix equation, called the
Covariance Extension Equation. This approach enables us to parameterize all
potential solutions using a monic Schur polynomial. Consequently, we extend our
result to the multivariable scenario and derive the necessary and sufficient
conditions for a group of $m\times m$ plants to be simultaneously stabilizable,
which can also be solved by our analytic interpolation method. Finally, we
construct four numerical examples, showcasing the application of our method
across various scenarios encountered in control systems engineering and
highlighting its ability to stabilize diverse systems efficiently and reliably.
