Continuity properties of solutions to $H_2$ and $H_\infty$ Riccati equations

Abstract

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 nonleft-invertibility and, in contrast to what one might think, unrelated to zeros on the imaginary axi