Feedback Stabilization of a Class of Unstable Nonholonomic Systems

Abstract

This paper considers the design of nonlinear stabilizing controllers for a class of systems which exhibit unstable rolling dynamics or shimmy. Such systems can be used, for example, to approximate the complex dynamics of an aircraft landing gear structure. The controllers are designed using the well-known nonlinear control technique known as feedback linearization and some recent results pertaining to stability of hybrid systems. We consider three models of a system exhibiting shimmy, each progressively more sophisticated than the other and in each case we derive the controllers that stabilize the system. An interesting conclusion of this study is that the models that are more complex can be stabilized with simpler controllers.