Parametrization of algebraic numerical differentiators to achieve desired filter characteristics

Synthesis on a class of algebraic differentiators and application to nonlinear observation

“…The largest difficulty is to chose the parameter T (the length of the sliding integration window), which depends on the nature of the signal to differentiate and the one of noises. Hence, as shown in [22], a criterion should be considered in order to choose an appropriate value of T . This is beyond the scope of this paper.…”

“…Hence, a criterion should be considered in order to choose an appropriate value of T (see, e.g. [22]). This is beyond the scope of this paper.…”

Algebraic estimation of impact times: Juggling a ball with a magnetically levitated plate

“…Neither precise mechanical components nor additional sensors that measure the ball position are used. An extension of the faultdiagnosis methods discussed in [8], [9] is used to detect previous collisions in order to predict the next collision. The predictions must be accurate and precise due to limitations of the achievable displacements and actuator dynamics.…”

Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs

“…✷ Error analysis for the estimation u e given in Proposition 1 can be given thanks to previous studies. On one hand, according to (11), the estimation u e contains a truncated term error (see [8,9] for more theoretical analysis). On the other hand, according to (12), the truncated term error in (11) is a source of error forλ t,i .…”

“…The latter has been also extended to many applications, such as parameter estimation for noisy signals (see, e.g., [2,3,4,5,6]), and numerical differentiation (see, e.g., [7,8,9,10,11]). The main idea of this method is to apply some algebraic operations (such as differentiation and multiplication) to a linear differential equation of the analyzed signals in the Laplace operational domain.…”