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On Bounds for the Solution of the Riccati and Lyapunov Equations

In recent years, several bounds have been reported for different measures of the “extent” or “size” of the solution of the algebraic matrix equation arising in control theory, such as the Riccati equation and the Lyapunov equation. This paper collects the bounds that have been presented up to now and summarizes them in an unified form. This will prove particularly convenient for those wishing to get a ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds. Key-Words: Algebraic Riccati equation, algebraic Lyapunov equation, upper and lower bounds. * This work was supported by the KBN under Grant 8T 11A 028 18