International Journal of applied mathematics and computer science

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Paper details

Number 2 - June 1998
Volume 8 - 1998

μ-Analysis and robust stability of positive linear systems

Diederich Hinrichsen, Nguyen K. Son

In this paper, we develop a μ-analysis for nonnegative matrices and apply the results to analyse robust stability of positive linear continuous-time systems under arbitrary affine parameter perturbations. It is shown that real and complex stability radii of positive systems coincide for arbitrary affine perturbation structures, in particular for block-diagonal disturbances. Estimates and computable formulae are derived for these stability radii. The results hold for arbitrary perturbation norms induced by absolute vector norms (e.g. p-norms, 1 ≤ p ≤ ∞).