Input-output stability implies exact linearization

Abstract EN

We study the recently introduced notion of input output stability, which is a robust variant of the minimum phase property for general smooth nonlinear control descriptor systems.

This paper develops the theory of input-output stability in the single-input, single-output setting.

We knew that if a descriptor system has a uniform M vector relative degree and is detectable through the output and its derivatives up to some order, uniformly over all inputs that produce a given output, then it is input-output stable.

In this paper we show that the converse is also true, thus arriving at a useful equivalent characterization of input-output stability.

In this paper, exact linearization via state feedback and stabilization for affine descriptor systems are considered.

Using a local diffeomorphism and a state feedback, the affine descriptor system is transformed to a linear normal form system.

Choosing appropriate feedback controller, the closed-loop system is asymptotically stabilized.