Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system

Abstract

This paper presents the H ∞ static output feedback control of nonlinear fractional-order systems. Based on the extended bounded real lemma, the H ∞ control is formulated and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belongs to 0 < α < 1. The control approach is finally applied to the regulation of the glucose level in diabetes type 1 treatment. Therefore, it is attempted to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of the system in the presence of meal disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance.

Using the fractional order calculus in the combination of the MIT and Lyapunov stability method

“…In the specialized literature, there are many papers which present how the fractional order calculus can be used to control a dynamical system [1][2][3][4] (see the Model Reference Adaptive System (MRAS) [5][6][7][8][9][10][11]). Introducing the fractional order calculus in the adaptive control system leads to good performances.…”

H∞ Tracking Control for Nonlinear Fractional-Order Systems Via Output Feedback Design

“…Furthermore, concerning the extension of H∞ theory [24] to FO systems, analysis results on the computation of H∞ norm for FO system have recently been published in [6]. The H∞ state feedback and output feedback controllers for FO systems were proposed in [7] and [13], respectively. With the extension of Youla-Kucera parameterization, the H∞ control problem for LTI FO system was addressed in [14].…”

General Output Feedback Stabilization for Fractional Order Systems: An LMI Approach

“…Paradoxically, only few studies deal with OFC design for FOSs. One finds some existing results as presented in [27][28][29][30] only. Based on SVD method, [27] designs the OFC for a type of FOS with time delay.…”

“…Nevertheless, the SVD method is inherently conservative, particularly for such a large number of decision variables. Reference [28] designs an ∞ static OFC which is also based on SVD method, but the stable region reduced repeatedly in the transformation process. Reference [29] studies the FOS stabilization problem based on its approximation model, which does not face the original fractional order systems directly.…”