An SOS-QE Approach to Nonlinear Gain Analysis for Polynomial Dynamical Systems

Combined use of the method of sum of squares (SOS) and quantifier elimination (QE) is discussed with regard to the problem of nonlinear gain analysis for a class of dynamical systems. SOS, a numerical method, is used to search for the structure of a gain function quickly, and QE, a symbolic method, determines all gain functions in the structure to find the minimum gain function. QE can also be used for the infeasibility check of gain structures. A proposed analysis procedure for polynomial dynamical systems prevents unnecessary searching for a gain structure. Two illustrative examples show the effectiveness of the proposed gain analysis procedure.