Stability radii of linear functional differential equations. (Q1862729)

The authors discuss the robust stability of linear retarded systems which are described by the following linear functional-differential equation (FDE) \[ \dot{x}(t)= A_0x(t)+ \int_{-h}^{0}\,d[\eta(\theta)] x(t+\theta). \] A formula is derived for the complex stability radius of the system with respect to structured affine parameter perturbations. These results extend previous results for linear ordinary differential equations \(\dot{x}(t)=Ax(t)\) [\textit{D. Hinrichsen} and \textit{A. J. Pritchard}, Syst. Control Lett. 8, 105--113 (1986; Zbl 0626.93054) and \textit{N. K. Son} and \textit{D. Hinrichsen}, Numer. Funct. Anal. Optimization 17, 649--659 (1996; Zbl 0859.93046)] and those for linear retarded systems \(\dot{x}(t)=A_0x(t)+A_1x(t-h)\) [the authors, Acta Math. Vietnam. 24, 353--372 (1999; Zbl 0946.34067)].