NOVELTY - System (30) comprises: housing (42); a hydrogen storage element (46) enclosed within the housing; and a control system (40) for regulating storage of hydrogen into and retrieval of hydrogen from the solid-state hydrogen storage material.    USE - The system is useful: for storing and retrieving elemental hydrogen; in an auxiliary power unit for generating electrical power, where the auxiliary power unit is installed in the vehicle (all claimed); and in applications including powering fuel cells for vehicles, stationary power systems, and consumer electronics, and non-power applications including chemical production.    ADVANTAGE - The system is capable of: achieving a full or nearly-full recharge, thus reducing the cost of owning and operating the hydrogen storage system; and significantly increasing the practicality, functionality and economics of solid-state hydrogen storage systems.    DETAILED DESCRIPTION - System (30) comprises: housing (42); a hydrogen storage element (46) enclosed within the housing; and a control system (40) for regulating storage of hydrogen into and retrieval of hydrogen from the solid-state hydrogen storage material. The hydrogen storage element comprises a solid-state hydrogen storage material, where at least a portion of the solid state hydrogen storage material comprises: a porous matrix material comprising atoms of a first element capable of bonding with more than one hydrogen atom (22) per atom of the first element, where the atoms of the first element are molecularly arranged within the porous matrix material so that different atoms of the first element have bond sites available for different numbers of hydrogen atoms at correspondingly different levels of bonding energy; hydrogen atoms molecularly bonded to atoms of the first element, where some atoms of the first element have more hydrogen atoms bonded to it than other atoms of the first element; and atoms of a second element capable of molecularly bonding to atoms of the first element and the hydrogen atoms, where the atoms of the second element are bonded to those atoms of the first element having bond sites for more than one hydrogen atom and as a consequence at lower bond energies than the bond sites of those atoms of the first element to which a fewer number of hydrogen atoms are bonded. INDEPENDENT CLAIMS are also included for:    (1) the auxiliary power unit having the system; and    (2) the vehicle having auxiliary power unit.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic representation of hydrogen storage and retrieval systems capable of using porous storage materials and performing hydrogenation and dehydrogenation processes.    Hydrogen atom (22)    System for storing and retrieving elemental hydrogen (30)    Control system (40)    Housing (42)    Hydrogen storage element (46)