Sampled-data stabilisation of a class of state-delayed nonlinear dynamics

Abstract

The paper deals with the stabilisation of strictfeedback dynamics with a delay on the last component of the state. It is shown that the Immersion and Invariance approach provides a natural framework for solving the problem. An accademic simulated example is provided.

Nonlinear Sampled-Data Stabilization with Delays

“…The following result generalizes Theorem 3.1 in [18] Theorem 5. Consider the continuous-time dynamics (10) with τ = Nδ .…”

“…Then (1) is sampleddata I&I stabilizable; i.e. its sampled equivalent dynamics (17) is I&I stabilizable with target dynamics (18).…”

“…The purpose of this work is to go further in the direct design of sampled-data feedback laws for input-delayed dynamics and investigate some simple extensions to special classes of systems affected by state delays. The results stated by the authors for the class of input-affine dynamics in some recent works [16,17,18,19] are in the sequel extended to more general classes of nonlinear time-delayed systems with several comments on some open perspectives. Throughout the paper we address the problem of designing sampled-data controllers of a given continuous input-delayed dynamics starting from its sampled equivalent model; the resulting control laws admit parametrized expressions in the sampling period which can be used to underline the possible advantage of sampling.…”

Immersion and invariance stabilization of strict-feedback dynamics under sampling

“…This result has been applied for stabilization of strict-feedback systems with state delay (Mattioni, Monaco, & Normand-Cyrot, 2015a). Work is progressing to relax the ''strict-feedback'' assumption and extend the result to general nonlinear systems in input-affine form.…”

Sampled-Data Reduction of Nonlinear Input-Delayed Dynamics

“…More recently, an increasing focus has been devoted to sampled-data time-delay systems (e.g, [10], [11]) when assuming that the control is piecewise constant and measures are available at discrete-time instants. This interest is mainly motivated by the fact that the retarded infinite dimensional continuous-time system admits a finite dimensional equivalent sampled-data model whenever there exists an explicit relation among the delay and the sampling period.…”