To cite this version: Denis Efimov, Johannes Schiffer. A new criterion for boundedness of solutions for a class of periodic systems. Abstract-A wide range of practical systems exhibits dynamics, which are periodic with respect to several state variables and which possess multiple invariant solutions. Yet, when analyzing stability of such systems, many classical techniques often fall short in that they only permit to establish local stability properties. Motivated by this, we present a new

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... ient criterion for global stability of such a class of nonlinear systems. The proposed approach is characterized by two main properties. First, it develops the conventional cell structure framework to the case of multiple periodic states. Second, it extends the standard Lyapunov theory by relaxing the usual definiteness requirements of the employed Lyapunov functions to signindefinite functions. D. Efimov is with with Inria, Non-A team, Parc Scientifique de la Haute Borne, A function V : R n → R is called sign-definite if V (0) = 0 and V (x) > 0 for all x ∈ R \ {0} or V (x) < 0 for all x ∈ R \ {0}; and it is called sign-indefinite if V (x) takes both, positive and negative, values.