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 spectral range from 3150 to 10000 A 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. 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++, N0/N+ and Ar/Si,S ratios, and computed dust corrections. Our analysis revealed that the DLA toward Q2343+12 requires important ionization corrections. 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 >= 8 kpc) or dwarf irregular galaxies (with a bursting or continuous star formation history) with ages varying from some 50 Myr only to >~ 3.5 Gyr and with moderate star formation rates per unit area of -2.1 < log psi < -1.5 M_{sol} yr^{-1} kpc^{-2}.
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