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IMPLICIT TRIANGULAR OBSERVER FORM DEDICATED TO A SLIDING MODE OBSERVER FOR SYSTEMS WITH UNKNOWN INPUTS

It has been presented in previous works that every uniformly observable single‐output system can be put on a triangular observation form. For this structure a special kind of sliding mode observer has been designed by authors, which ensures a finite‐time state reconstruction using a step by step observation algorithm. In this paper, we show that the multi‐output case is more delicate to study especially when the system has some unknown inputs. Thus, in order to generalizes the triangular observer form, from single to multi‐output case, we define an Implicit Triangular Observer (ITO) form. For such a form, two results are given. Firstly, we design a finite time converging observer for all values of the unknown inputs. Secondly, we give the necessary and sufficient condition, including a matching condition, for the existence of a coordinate change to put the system into this form. It is also shown that this class of systems is a subset of the uniform observable class of systems.