On the existence of upper bounds on the performance index of nonlinear systems

Abstract

Several interesting results are presented in determining the value of an integral performance index for certain types of finite changes in the characteristics of the system. In particular, we consider the assumed model of the system to be linear, while an accurate representation is given to a system containing a single nonlinearity. These assumptions, in many physical situations are quite reasonable. The performance index is specified as the integral of a quadratic function of the state of the system. Two theorems concerning the existence of upper-bounds for the values of the performance index are proved. Consideration of these theorems may lead to a meaningful insight into the relationship between changes in the system characteristics and the corresponding changes in the performance index.