This　paper　studies　a　dual　objective　control　problem　for　an　energy　storage　system　(ESS)　consisting　of　multiple　independently-controlled　energy　storage　units　(ESUs).　The　power　output　of　the　entire　ESS　is　designed　to　meet　its　reference,　and　meanwhile　the　state-of-energy　(SOE)　of　all　the　ESUs　maintains　to　be　balanced.　In　practice,　the　communication　among　ESUs　might　be　unreliable　and　thus　is　modeled　by　jointly　connected　switching　networks.　By　making　use　of　the　so-called　Generalized　Krasovskii-LaSalle　Theorem　together　with　a　novel　two-step　recursive　analysis　method,　it　is　rigorously　proven　that　the　dual　objective　control　problem　subject　to　jointly　connected　switching　networks　can　be　solved　by　a　consensus-based　distributed　control　algorithm.　(c)　2023　Elsevier　Ltd.　All　rights　reserved.