This paper proposes an analysis framework for robustness analysis of a nonlinear dynamics system that can be represented by a polynomial linear parameter varying (PLPV) system with constant bounded uncertainty. The proposed analysis framework contains three key tools: 1) a function substitution method which can convert a nonlinear system in polynomial form into a PLPV system, 2) a matrix-based linear fractional transformation (LFT) modeling approach, which can convert a PLPV system into an LFT system with the delta block that includes key uncertainty and scheduling parameters, 3) µ-analysis, which is a well known robust analysis tool for linear systems. The proposed analysis framework is applied to evaluating the performance of the LPV-fault detection and isolation (FDI) filters of the closedloop system of a transport aircraft in the presence of unmodeled actuator dynamics and sensor gain uncertainty. The robustness analysis results are compared with nonlinear time simulations.