For a positive switched system, the existence of a common linear copositive Lyapunov function (CLCLF) for the family of the subsystem matrices represents an important sufficient condition for its asymptotic stability. The main necessary and sufficient condition for the existence of a CLCLF (Fornasini and Valcher, IEEE Trans Autom Control 55:1933–1937, 2010, , Knorn et al, Automatica 45:1943–1947, 2009, ) consists in the explicit evaluation of the Hurwitz property of a family of \(p^n\) matrices, where p is the number of subsystems and n the size of each subsystem. In this paper we show that, when restricting our attention to compartmental switched systems, the Hurwitz property may be checked on a smaller subset of smaller matrices. Based on this result, we provide an algorithm that allows to determine whether a CLCLF exists, by simply checking the column sums of matrix sets of increasingly lower dimension and cardinality.
Positive switched system Compartmental model Linear copositive Lyapunov function
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