A brief summary of the bounds on the solution of the algebraic matrix equations in control theory

Abstract

Abstract In recent years, several bounds have been reported for different measures of the ‘ extent’ or ‘ size ’ of the solution of the algebraic matrix equations 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.