Stability Aspects of Exact Linearization Methods: A Hybrid Approach

In this paper, we examine from an input-output viewpoint, the feedback exact-linearization of nonlinear systems of the form x = f(x) + g(x)u, y = h(x). We show that exact-linearization through any kind of feedback cannot eliminate, but only relocate nonlinearity within the exact-linearizing feedback loop. In this work we establish that for a stable nonlinear system, stability of the system´s inverse is sufficient for stability of the exact-linearizing feedback loop, regardless of whether state or output, static or dynamic feedback is used. We also demonstrate that stability of the system´s inverse is sufficient but not necessary for stability of the exact-linearizing state-feedback loop. Finally, using an inner-outer type factorization of the original system, we provide necessary and sufficient conditions for stability of such a loop in a presence of unstable zero dynamics.