Modified Euler-Frobenius Polynomials With Application to Sampled Data Modelling

On partially minimum phase systems and nonlinear sampled-data control

“…The feedback control is in the form of a series expansion in powers of δ . Thus, iterative procedures can be carried out by substituting (17) into (16) and equating the terms with the same powers of δ (see [19] where the explicit expression for the first terms are given). Unfortunately, only approximate solutions γ [p] ( δ , x, v) can be implemented in practice through truncations of the series ( 17)) at finite order p in δ ; namely, setting γ [p] ( δ , x, v) = (γ 1[p] ( δ , x, v), .…”

“…and let the feedback (15) be the unique solution to the I-OM equality (16). Then the feedback u δ k = γ( δ , x k , v k ) ensures Input-Output linearization of ( 22) with stability of the internal dynamics.…”

“…As a consequence, the minimumphase property of a given nonlinear continuous-time system is not preserved by its sampled-data equivalent ( [9], [10], [11], [12]). To overcome those issues, several solutions were proposed based on different sampling procedures ( [10], [13], [14], [15], [16], [17]). Among these, the first one was based on multirate sampling in which the control signal is sampledfaster (say r times) than the measured variables.…”

“…Accordingly, this sampling procedure introduces further degrees of freedom and prevents from the appearance of the unstable sampling zero dynamics while preserving the continuoustime relative degree ( [9], [18]). As an alternative, in [13], [16] the authors exploited sampling via generalized hold function (GHF) in order to arbitrarily assign the zero-dynamics of the corresponding sampled-data equivalent system. Though, the relative degree is still not preserved in this case and the GHF method can be seen as a particular case of multirate sampling.…”

On partially minimum-phase systems and disturbance decoupling with stability

“…As a consequence, the minimum-phase property of a given nonlinear continuous-time system is not preserved by its sampled-data equivalent [28,29,30,31]. To overcome those issues, several solutions were proposed based on different sampling procedures [32,33,34,35,36,32,35]. Among these, the first one was based on multi-rate sampling in which the control signal is sampled-faster (say r times) than the measured variables.…”