In this paper, we design a model for the insurance pricing process of a portfolio of different (dependent or independent) non-life products. A standard decision function for the determination of the premium is proposed which use the recent claim experience and a negative feedback mechanism of the known surplus value. The model assumes a time-varying, bounded delay factor, time-varying parameters and different types of norm-bounded uncertainties. Finally, a Linear Matrix Inequality (LMI) criterion is derived for the investigation of the robust stability of the system. For the first time, a classical tool for the robust control analysis of engineering systems has been applied for the insurance pricing process of non-life products, extending further the existing literature. An example with 2 dependent non-life products illustrates the results of the paper.