Stability Analysis of Positive Switched Linear Systems With Delays

Asymptotic stability and decay rates of positive linear systems with unbounded delays

“…It is then natural to ask if the insensitivity properties of positive linear systems with respect to time delays will hold also for unbounded delays. In [14], it was shown that, for a particular class of unbounded delays, this is indeed the case. However, the question remains open for general classes of unbounded delays.…”

“…Note also that delays satisfying (2) may be unbounded. A particular class of unbounded delays was considered in [14] and is specified by Assumption 2.…”

“…Remark 2 Previous works in the literature established necessary and sufficient conditions for asymptotic stability of discrete-time positive linear systems, but required that the delays be either bounded (e.g., [11]- [13]), or unbounded under Assumption 2 [14]. It is clear that Assumption 1 covers all these classes of time-delays as special cases.…”

“…However, the question remains open for general classes of unbounded delays. Moreover, the impact of unbounded delays on the decay rate of positive linear systems was not considered in [14]. This paper closes these gaps.…”

“…At the core of our paper is a set of powerful conditions for delay-independent stability of discrete-time positive linear systems with heterogeneous unbounded time-varying delays. Our proof technique, which neither uses the LyapunovKrasovskii functional method used in [11] nor the approach used in [14], allows us to impose minimal restrictions on delays. More specifically, we make the following contributions.…”