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Positively invariant sets for constrained continuous-time systems with cone properties

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2 Author(s)
Tarbouriech, S. ; Lab. d''Autom. et d''Anal. des Syst., CNRS, Toulouse, France ; Burgat, C.

This note deals with some properties of particular bounded sets w.r.t. linear continuous-time systems described by x˙(t)=A(0)x(t)+c(t), where c(t)∈Ω⊂Rn, Ω a compact set, and matrix etA(0) has the property of leaving a proper cone K positively invariant, that is etA(0)K⊂K. The considered bounded sets 𝒟(K; a, b) are described as the intersection of shifted cones. Necessary and sufficient conditions are given. They guarantee that such sets are positively invariant w.r.t. the considered system. The trajectories starting from x 0∈Rn/𝒟(K; a, b) (respectively to x0 ∈Rn) are studied in terms of attractivity and contractivity of the set 𝒟(K; a, b). The results are applied to the study of the constrained state feedback regulator problem

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Automatic Control, IEEE Transactions on  (Volume:39 ,  Issue: 2 )