Robustness of exponential stability of a class of switched positive linear systems with time delays

This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations (FDE) under arbitrary switching or average dwell time switching. We will measure the stability robustness of such a system (which is considered as a nominal system) subject to parameter affine perturbations of its constituent subsystems matrices, by introducing the notion of structured stability radius. Some formulas for computing this radius, as well as estimating its lower bounds and upper bounds, are established. In the case of switched linear systems with multiple discrete time-delays or/and distributed time-delays, the obtained results yield tractably computable formulas or bounds for the stability radius. The extension of the obtained results to non-positive systems and the class of multi-perturbations has been presented. Examples are given to illustrate the proposed method.

Automated summary

This paper investigates the robustness of exponential stability of positive switched systems described by linear functional differential equations under arbitrary or average dwell time switching. It introduces the notion of structured stability radius to measure the stability robustness of the system subject to parameter affine perturbations. It establishes formulas for computing this radius and estimating its lower bounds and upper bounds. The results provide tractably computable formulas or bounds for the stability radius in the case of switched linear systems with multiple discrete time-delays or/and distributed time-delays. The extension of the obtained results to non-positive systems and the class of multi-perturbations is also presented.