Observers and output differentiators in uncertain systems (Q2577250)

In the first part of the paper, the authors review some results about observability and observer construction for single-input-single-output linear time-invariant systems \[ \dot x= Ax+ b\psi,\quad y= cx, \] where \(\psi\) is interpreted as an uncertain input, with \(|\psi|\leq q\| x\|\) for some known constant \(q\). The system \((A, b, c)\) is assumed controllable and observable, and its zeros are on the left-hand complex plane. In the second part, the authors deal with nonlinear systems on a differentiable manifold \(M\), \[ \dot x= f(x),\quad y= h(x). \] They prove some tests for observability; then, for systems which satisfy the rank observability condition, they propose a construction for both an observer and an output differentiator (i.e., an estimator of the derivatives of the output). The results are applied to the estimation of the angular velocity of a mathematical pendulum.