This paper addresses the problem of H-similar to performance controller parameterisation for a plant switching amongst a finite family of given configurations. It is assumed that switching is uncontrolled, namely governed by some arbitrary switching rule, and that the controller has the information of the current configuration. Based on Riccati inequalities, there exists a set of controller parameterisation which ensures that the closed-loop switching linear system under uncontrolled switching achieves certain H-similar to controlled performance.