Robustification of sample-and-hold stabilizers for control-affine time-delay systems

On emulation of observer-based stabilizers for nonlinear systems

“…In this section, we present our main result concerning sampled-data stabilization for nonlinear time-delay systems, stabilized by continuous-time observerbased controllers. In particular, taking into account the stabilization in the sample-and-hold sense theory (see [8], [35], [36], [37]), it is shown that, under suitable conditions: there exists a minimal sampling frequency (aperiodic sampling is allowed) such that, by Euler emulation of an observer-based controller, semi-global practical stability, with arbitrary small final target ball of the origin, is guaranteed.…”

“…In this approach, a continuous-time controller for the system at hand is firstly designed, ignoring sampling, and then, it is implemented digitally. Sampled-data stabilization of linear, bilinear and nonlinear systems, even infinite dimensional ones, has been studied in the literature by many approaches, such as: i) the time-varying delay approach (see [9], [10] and [11]), ii) the approximate system discretization approach (see [3], [14], [23], [26], [27], [28], [29], [33], [41], [42], [43], [44]), iii) the hybrid system approach (see [1] [2], [16], [24], [25], [30], [31], [32]); iv) the stabilization in the sample-and-hold sense approach (see [5], [6], [7], [8], [34], [35], [36], [37]). The reader can refer to [17] for an interesting survey on the topic.…”

Robust global nonlinear sampled-data regulator for the Glucose-Insulin system

“…Furthermore, here we take into account observation errors in the measurements of glucose and insulin concentrations, and disturbances d (t), affecting the insulin delivery rate and the mechanism actuating the insulin pump. In order to attenuate the effects of such disturbances and errors, we make use of the recent results about the ISS redesign methods in the framework of stabilization in the sample-and-hold sense theory (see [7], [8], [32], and, for the continuous-time case, see [33], [36]).…”

“…Sampled-data stabilization has been studied in the literature by many approaches, such as: i) the time-varying delay approach (see for instance [11]), ii) the approximate system discretization approach (see [18], [19]), iii) the hybrid system approach (see [2], [20]); iv) the stabilization in the sample-and-hold sense approach (see [5], [8], [29]). The notion of stabilization in the sample-and-hold sense, introduced in 1997 in [5], has been widely studied for systems described by ordinary differential equations, and recently extended to systems with delays too (see [7], [8], [28] and [29]). In this paper, taking into account the results in [7], concerning the stabilization in the sample-and-hold sense for nonlinear time-delay systems, a robust nonlinear global state-feedback stabilizer for the DDE model of the glucoseinsulin system is provided.…”

“…In this paper, taking into account the results in [7], concerning the stabilization in the sample-and-hold sense for nonlinear time-delay systems, a robust nonlinear global state-feedback stabilizer for the DDE model of the glucoseinsulin system is provided. The proposed global sampleddata controller is based on the theory of Sontag's stabilizers (see [17], [30] and [35]) and on the recent results about stabilization in the sample-and-hold sense for nonlinear timedelay systems (see [7], [8], [28] and [29] and reference therein). The feedback control law shows good performances for sampling periods comparable to the ones available for usual glucose sensors, with the robustified sampled-data state feedback that can cope with the effect of significant actuation disturbances and measurement errors affecting both the glucose and insulin concentrations.…”