Stability radius of second order linear structured differential inclusions

摘要

For arbitrary second order square matrices $A, B, C$; $A$ Hurwitz stable, the minimum positive value $R$ for which the differential inclusion $$dot{x}in F_{R}(x):={(A+BDelta C)x, Delta in mathbb{R}^{2imes 2}, |Delta | le R }$$ fails to be asymptotically stable is calculated, where $| cdot |$ denotes the operator norm of a matrix.