Modeling of nonlinear system uncertainties using a linear fractional transformation approach

This paper proposes a technique to model uncertain nonlinear systems whose models vary due to changes in the system configuration and operating conditions. To represent these variations in linearized models, the system state-matrices are expressed as matrix polynomials in the uncertain parameters. The representation of matrix polynomials in the form of a linear fractional transformation (LFT) is discussed, and algorithms based on controllability and observability conditions and singular value decomposition are proposed to reduce the order of the LFT form. The reduced LFT form of the state-matrices are then used in the state-equations to obtain a system model in the standard form. A power system model is used to illustrate this uncertainty modeling approach.