By combining our UVES-VLT spectra of a sample of four damped Ly \alpha systems ( DLAs ) toward the quasars Q0100+13 , Q1331+17 , Q2231 - 00 and Q2343+12 with the existing HIRES-Keck spectra , we covered the total optical spectral range from 3150 to 10 000 Å for the four quasars .
This large wavelength coverage and the high quality of the spectra allowed us to measure the column densities of up to 21 ions , namely of 15 elements - N , O , Mg , Al , Si , P , S , Cl , Ar , Ti , Cr , Mn , Fe , Ni , Zn .
This comprehensive set of ionic column densities and elemental abundances severely contrasts with the majority of DLAs for which only a handful of ions and elements is typically observed .
Such a large amount of information is necessary to constrain the photoionization and dust depletion effects , two important steps in order to derive the intrinsic chemical abundance patterns of DLAs .
We evaluated the photoionization effects with the help of the Al ^ { + } /Al ^ { + + } , Fe ^ { + } /Fe ^ { + + } , N ^ { 0 } /N ^ { + } and Ar/Si , S ratios , and computed dust corrections .
Our analysis revealed that the DLA toward Q2343+12 requires important ionization corrections .
This makes the abundance determinations in this object uncertain .
The access to the complete series of relatively robust intrinsic elemental abundances in the other three DLAs allowed us to constrain their star formation history , their age and their star formation rate by a detailed comparison with a grid of chemical evolution models for spiral and dwarf irregular galaxies .
Our results show that the galaxies associated with these three DLAs in the redshift interval z _ { abs } = 1.7 - 2.5 are either outer regions of spiral disks ( radius \geq 8 kpc ) or dwarf irregular galaxies ( showing a bursting or continuous star formation history ) with ages varying from some 50 Myr only to \gtrsim 3.5 Gyr and with moderate star formation rates per unit area of -2.1 < \log \psi < -1.5 
M _ { \odot } yr ^ { -1 } kpc ^ { -2 } .