Continuity properties of solutions to H2 and H∞ Riccati equations

In H2 and H8 optimal control (semi-)stabilizing solutions of algebraic Riccati equations play an essential role. It is well-known that these solutions might have discontinuities as a function of the system parameters. The paper shows that these discontinuities are directly linked to non-left-invertibility and, in contrast to what one might think, unrelated to zeros on the imaginary axis.