Stability radii of positive higher order difference system in infinite dimensional spaces

In this paper we study stability radii of positive higher order difference system under affine perturbations of the coefficient operators. It is shown that the real and complex stability radii coincide. Moreover, explicit formulas are derived for these stability radii and illustrated by some examples. The results obtained are extensions of the recent work in [D. Hinrichsen, P.H.A. Ngoc, N.K. Son, Stability radii of positive higher order difference system, Systems Control Lett. 49 (2003) 377–388] to Banach spaces.