Preservation of solvability conditions in Riccati equations when applying SPR0 substitutions

We are concerned by algebraic Riccati equations associated to robust control problems. We tackle the preservation of solvability conditions of algebraic Riccati equations when applying substitutions of the Laplace variable s by some class of strictly positive real functions in the corresponding single-input and single-output transfer functions. In particular, we study the preservation of solvability conditions associated to the existence of stabilizing solutions of algebraic Riccati equations characterized by an H^∞-norm constraint on a particular linear time-invariant system. We illustrate our results with the study of the closed-loop stability of a family of linear time-invariant systems, affected by time-varying uncertainty, controlled via robust sliding mode control.