Stability radius of second order linear structured differential inclusions

Abstract

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

Keywords

• robust stability
• stability radius
• differential inclusions
• ordinary differential equations
• qualitative theory
• perturbation theory