Analysis and Design of Output Feedback PD Controllers for Time-Delay Systems

Pieter Appeltans (1) , Silviu-Iulian Niculescu (2, 3) , Wim Michiels (1)

1 Department of Computer Science - K.U.Leuven
2 L2S - Laboratoire des signaux et systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

In this paper we analyze proportional-derivative output feedback control for single-input single-output linear time-invariant dynamical systems with discrete state delays. The main focus of the presented work is the analysis of the effect of arbitrarily small implementation errors, such as a feedback delay or a finite-difference approximation of the derivative, on the stability of the closed loop. More specifically, it will be shown that the classical notion of stability does not suffice to adequately describe the asymptotic behavior of the closed loop system in the presence of these implementation errors, as stability might be lost even when these errors are made arbitrarily small. This paper therefore considers strong stability, which eliminates this well-posedness problem by not only requiring stability but by also enforcing that stability is preserved for sufficiently small perturbations. To conclude this paper, a controller design methodology for proportionalderivative output feedback controllers that strongly stabilize the system, is proposed.

Domains: Engineering Sciences [physics]

Pieter Appeltans, Silviu-Iulian Niculescu, Wim Michiels. Analysis and Design of Output Feedback PD Controllers for Time-Delay Systems. ECC 2021 - European Control Conference, Jun 2021, Rotterdam / Virtual, Netherlands. ⟨10.23919/ecc54610.2021.9655198⟩. ⟨hal-03191808⟩