Multivariable simultaneous stabilization: A modified Riccati approach

Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case. The method utilizes a Riccati-type matrix equation known as the Covariance Extension Equation, which yields all solutions parameterized in terms of a matrix polynomial. The procedure is demonstrated through specific examples.