An SOS-QE approach to nonlinear gain analysis

A hybrid computational method between sum of squares (SOS) and quantifier elimination (QE) is discussed for a problem of nonlinear gain analysis. A computational procedure is proposed to be applied to nonlinear polynomial systems. The procedure takes two major parts: the first part is searching a structure in the gain functions while the second part reveals all the gain functions in the structure. These tasks are assigned to the SOS and QE approaches, respectively. In order to find an accurate system performance, the gain functions are optimized in the procedure. The proposed analysis procedure is illustrated for a few systems.