%0 Conference Proceedings %T Computing capture tubes %+ Département STIC [Brest] (STIC) %+ Lab-STICC_ENSTAB_CID_IHSEV ; OSM %+ Theory, Algorithms and Systems for Constraints (TASC) %+ MBDA (MBDA-F) %+ Department of Physics %A Jaulin, Luc %A Ninin, Jordan %A Chabert, Gilles %A Menec, Stéphane Le %A Seddik, Mohamed Saad Ibn %A Doze, Vincent Le %A Stancu, Alexandru %< avec comité de lecture %B SCAN 2014 %C Wurzburg, Germany %8 2014-09-21 %D 2014 %K capture tube %K contractors %K interval arithmetic %K robotics %K stability. %Z Engineering Sciences [physics]/Automatic %Z Mathematics [math]/Information Theory [math.IT]Conference papers %X A dynamic system can often be described by a state equation ˙x = h(x, u, t)where x ∈ Rn is the state vector, u ∈ Rm is the control vector and h :Rn × Rp × R → Rn is the evolution function. Assume that the control lowu = g (x, t) is known (this can be obtained using control theory), the systembecomes autonomous. If we define f (x, t) = h(x, g (x, t) , t), we get the followingequation.˙x = f (x, t) .The validation of some stability properties of this system is an important anddifficult problem [2] which can be transformed into proving the inconsistency of aconstraint satisfaction problem. For some particular properties and for invariantsystem (i.e., f does not depend on t), it has been shown [1] that the V-stabilityapproach combined interval analysis [3] can solve the problem efficiently. Here,we extend this work to systems where f depends on time. %G English %L hal-01122023 %U https://hal.science/hal-01122023 %~ UNIV-NANTES %~ ENSTA-BRETAGNE %~ MINES-NANTES %~ CNRS %~ INRIA %~ INRIA-RENNES %~ LINA %~ ENSTA-BRETAGNE-STIC %~ INSMI %~ LINA-TASC %~ INRIA_TEST %~ TESTALAIN1 %~ INFO %~ LAB-STICC %~ INRIA2 %~ TDS-MACS %~ LS2N-TASC-IMTA %~ IMTA_DAPI %~ LAB-STICC_IMTA %~ LS2N-IMTA %~ INRIA-RENGRE %~ IMT-ATLANTIQUE %~ NANTES-UNIVERSITE %~ UNIV-NANTES-AV2022