Robust stability of positive linear time-delay systems under affine parameter perturbations
A dynamical system in \(\mathbb{R}^{n}\) is called positive if any trajectory starting in the positive ortant \(\mathbb{R}_{+}^{n}\) always remains in \(\mathbb{R}_{+}^{n}\). The authors study the robust stability of linear uncertain positive time-delay systems under affine perturbations \[ \dot x(t)=(A_{0}+D_{0}\Delta_{0}E_{0})x(t)+ (A_{1}+D_{1}\Delta_{1}E_{1})x(t-h), \] where \(A_{i},D_{i},E_{i}\), \(i=0,1\), are given matrices, \(\Delta_{0},\Delta_{1}\) are unknown disturbance matrices whose sizes are measured by operator norms \(\|\Delta_{0}\|,\|\Delta_{1}\|\). The paper extends results of \textit{D. Hinrichsen} and \textit{A. J. Pritchard} [Syst. Contr. Lett. 7, 1-10 (1986; Zbl 0631.93064)] and \textit{D. Hinrichsen} and \textit{N. K. Son} ]Appl. Math. Comp. Sci. 8, No.~2, 253-268 (1998; Zbl 0914.93051)] to positive linear time-delay systems.
scientific article; zbMATH DE number 1406567