Passivity and Unknown Input Observers for Nonlinear Systems

The main objective of this work is to study the relationship between passivity and existence of UIO in the nonlinear case. This work is motivated by two facts: On the one side by the well-known relationship between passivity and robustness in control theory. On the other side the equivalence previously found by one of the authors in the linear (square) case between three concepts: existence of Unknown Input Observers (UIO), existence of a state feedback that renders the system strictly passive (SFSP), and existence of an output injection that makes the system strictly passive (OISP). We will restrict ourselves to the global study of square nonlinear systems (the number of unknown inputs is equal to the number of outputs), and assume that the system has only unknown inputs that enter linearly in the state equation. These assumptions simplify the analysis but none is essential. We will show that in the nonlinear case, under some regularity assumptions, the existence of UIO implies SFSP and OISP. But the converse is not valid in general. This means that in general existence of UIO is a stronger property than passificability, in contrast to the situation in the linear case.