On emulation of observer-based stabilizers for nonlinear systems

Abstract

In this paper, we deal with the problem of the stabilization in the sample-andhold sense, by emulation of continuous-time, observer-based, global stabilizers. Fully nonlinear time-delay systems are studied. Sufficient conditions are provided such that the Euler approximation of continuous-time, observer-based, global stabilizers, for nonlinear time-delay systems, yields stabilization in the sample-and-hold sense. Submitted (in an extended version) to Automatica.

Semiglobal Sampled-Data Dynamic Output Feedback Controller for the Glucose–Insulin System

“…By properly exploiting the theory on the stabilization in the sample-and-hold sense (see [5], [6]), as applied to time-delay systems (see [12], [36] and [38]), a semi-global nonlinear sampled-data output controller for system (2) is designed in order to reduce the high basal plasma glucose concentration to the reference glucose value.…”

“…Before to state the main theoretical results related to the closed-loop system constituted by the DDE glucose-insulin model ( 2) in closed-loop with v(t) = v(t j ), t j ≤ t < t j+1 (see Euler emulation ( 6)), we introduce the following standard assumptions (see [12], [10], [11], [36], [38], [37]), which will be useful to tune the control parameters.…”

“…The proof is based on recent results on the stabilization in the sample-and-hold sense (see [12], [11], [36]). As a preliminary step it is useful to rewrite system (2) with respect to the displacement…”

“…Sampled-data stabilization has been studied in the literature according to many approaches, such as: i) the time-varying delay approach (see for instance [17]), ii) the approximate system discretization approach (see [26], [27]), iii) the hybrid system approach (see [2], [28]); iv) the stabilization in the sample-and-hold sense approach (see [5], [6], [12], [10], [11], [36], [38], [37]). To implement sample-data regulators by emulation is often the common choice in practical applications, and its philosophy is shared by some of the aforementioned approaches, like the hybrid and the sample-and-hold sense ones.…”

“…In these frameworks, emulation consists in (i) first designing a continuous-time controller for the system at hand, and then, (ii) discretizing it in order to make use of sampleddata measurements and to apply the control law by zero-order hold devices. The notion of stabilization in the sample-andhold sense, introduced in 1997 in [6], has been widely studied for systems described by ordinary differential equations, and recently extended to systems with delays too (see [12], [10], [36] and [38]). Based on these recent results, the sampled-data (by Euler emulation) output dynamic regulator is applied, in this paper, to the DDE model of the glucose-insulin system with the aim of glucose control.…”