Relative degree of interconnected SISO nonlinear control systems

Abstract

The concept of relative degree plays an important role in nonlinear control theory. It provides, for example, a necessary and sufficient condition for the existence of a feedback linearizing control law for a single-input, single-output (SISO) input-affine nonlinear state space system. It also gives a sufficient condition under which a left inverse exists. In applications it is common for systems to be composed of smaller interconnected subsystems. It is known that various feedback structures preserve relative degree, but it is largely unknown how to compute the relative degree of interconnected systems using only their properties. So the goal of this paper is to determine the relative degree of two nonlinear control systems interconnected in a variety of different ways. A collection of illustrative examples is given.