Design of the discontinuous observers

This paper gives a new formulation of the robust observers for the minimum phase dynamical systems with arbitrary relative degrees (with respect to the relation between disturbance-output) by applying the implicit observer techniques. For plants with relative degree one, the robust observer is constructed without any a priori on the disturbance. For plants with relative degree two, an identification of the integral of the disturbance is made by using the variable structure approach, the state vector is asymptotically expressed by the integrals of the input and output and the estimation of the integrals of the disturbance. For plants with relative degree higher than two, the observer formulation is stated as a conjecture. Numerical examples and simulation results are presented to show the effectiveness of the proposed algorithms.