An LMI-based Analysis of Stability Margins in Adaptive Flight Control

In this paper we show that, by casting the error dynamics of an adaptive control system into a Linear Parameter Varying form, we can apply linear matrix inequality techniques and calculate stability margins for adaptive control systems. More precisely, by taking the viewpoint that nonlinear systems, in particular some classes of adaptive controllers, can be parameterized by a set of linear systems, we show that stability margins defined in linear robust control theory can be analyzed. Whereas the concept of gain-margin is clear whether a system to be analyzed is linear or nonlinear, frequency responses for general nonlinear systems are not defined, and therefore in this paper we consider time-delay margin instead of phase-margin in our formulation. Theoretically guaranteed margins are verified using the Generic Transportation Model simulation provided by NASA Langley.