This article deals with the problem of synthesis of optimal by the minimal value of integral-quadratic criterion dynamic systems, which are described by a model of equations in state variables.
A modeling problem of the process of liquid multi component decontamination by a spatial filter is considered, it takes into account the reverse influence of decisive factors (contamination concentrations of liquid and sediment) on characteristics (coefficient of porosity, diffusion) of the medium and gives us the possibility to determine small mass transfer coefficient under the conditions of prevailing of convective constituents over diffusive ones.