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Asymptotic stability and stabilizability of special classes of discrete-time positive switched systems. (English) Zbl 1258.93091

Summary: In this paper, we consider discrete-time positive switched systems. Switching is appearing among autonomous subsystems, characterized either by monomial matrices or by circulant matrices. Necessary and sufficient conditions are provided guaranteeing either (global uniform) asymptotic stability or stabilizability (i.e. the possibility of driving to zero the state trajectory corresponding to any initial state by resorting to some switching sequence). Such conditions lead to simple algorithms that allow to easily detect, under suitable conditions, whether a given positive switched system is not stabilizable.

MSC:

93D20 Asymptotic stability in control theory
93C55 Discrete-time control/observation systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
15B48 Positive matrices and their generalizations; cones of matrices
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