A symbolic-numeric approach to nonlinear gain analysis of a class of dynamical systems

It is an important task to obtain a nonlinear gain function of dynamical systems by computational methods. A numerical approach, sum of squares (SOS), has been proposed so far, but there is no clue to find a minimum one. In this paper, a procedure is proposed to analyze nonlinear gain functions of a class of dynamical systems by combination use of symbolic and numeric methods. The role of SOS is to search for a structure of a gain function quickly and then quantifier elimination (QE) covers all possible functions in the structure to find a minimum function. An illustrative example shows the effectiveness of the proposed analysis procedure.