Guaranteed Cost Control of Genetic Regulatory Networks With Multiple Time-Varying Discrete Delays and Multiple Constant Distributed Delays

Xian Zhang,Chunyan Liu,Yantao Wang,Zhiwei Zhang

doi:10.1109/access.2020.2987650

Abstract

This paper focus on the problem of guaranteed cost control for a class of genetic regulatory networks with multiple time-varying discrete delays and multiple constant distributed delays. Firstly, a novel method is proposed to establish a sufficient condition for the existence of guaranteed cost controller. The sufficient condition includes only several simple inequalities, which can easily solved by standard tool softwares, such as MATLAB. Secondly, the desired guaranteed cost controller is designed based on the solution of these inequalities. Thirdly, the proposed method is also available to the stabilization problem of genetic regulatory networks under consideration. Finally, the results of two numerical examples demonstrate the applicability of theoretical results. Compared with the existing results, this present paper has three merits: (i) Do not require to construct any Lyapunov-Krasovskii functional; (ii) the class of genetic regulatory networks under consideration is more general; (iii) the designed controller can be easily realized.

Highlights

As one class of complex dynamic nonlinear systems, genetic regulation networks (GRNs) describe the interactions among mRNAs and proteins in gene expression [1], [2]
Remark 3: There are three differences between [8] and the present paper: (i) The Lyapunov–Krasovskii functional (LKF) method is used in [8], while no LKF is required in this paper; (ii) The GRN model in this paper is more general than one in [8]; and (iii) The guaranteed cost controller designed in this paper can ensure the global exponential stability of the resulting closed-loop system, but only asymptotic stability can be guaranteed in [8]
This paper has dealt with the GCC problem of GRNs with multiple time-varying discrete delays and multiple constant distributed delays

Summary

INTRODUCTION

As one class of complex dynamic nonlinear systems, genetic regulation networks (GRNs) describe the interactions among mRNAs and proteins in gene expression [1], [2]. To decrease the computational complexity of the method, the linear matrix inequality (LMI) method is used to solve the GCC problem time-delay systems (see, e.g., [8], [15], [19]). Functional differential/difference equations have been employed to model GRNs. It is well known that time delays often result in poor performance and/or instability in dynamical. The applicability of the proposed method is presented by a pair of numerical examples Compared with these mentioned literature on the control problems of delayed GRNs, this present paper has the following advantages: (i) No LKF requires to be constructed; (ii) the GRN model under consideration is more general; (iii) the proposed method to design controller can be realized.

PROBLEM FORMULATION

GUARANTEED COST CONTROLLERS

AN ILLUSTRATIVE EXAMPLE

CONCLUSION