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Relationships between asymptotic stability and exponential stability of positive delay systems. (English) Zbl 1282.93214
Summary: This paper explores the relations between asymptotic stability and exponential stability of continuous-time and discrete-time positive systems with delay. A system is said to be positive if its state and output are non-negative whenever the initial condition and input are non-negative. Two results are obtained. First, if a positive system is asymptotically stable for all bounded (further continuous, for continuous-time systems) time-varying delays, then it is exponentially stable for all such delays. In particular, if a positive system is asymptotically stable for a given constant delay, then it is exponentially stable for all constant delays. Second, if the involved delays are unbounded, then the positive system may be not exponentially stable even if it is asymptotically stable.

MSC:
93D20 Asymptotic stability in control theory
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
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