State bounding and controller design for genetic regulatory networks with multiple delays and bounded disturbances

Abstract

This article addresses the problems of state bounding and state‐feedback controller design for genetic regulatory networks with multiple delays and bounded disturbances. Multiple time‐varying discrete delays and multiple constant distributed delays are involved. A delay‐dependent sufficient condition containing several simple inequalities is first given to guarantee that the state trajectories remain inside or converge exponentially into a Cartesian product of two polytopes. Furthermore, equivalent sufficient conditions directly represented by the system parameters are derived. Based on the state bounding results, one can obtain reachable set estimation and global exponential stability criteria. By designing state‐feedback controllers, the state trajectories of the close‐loop system are limited in a given Cartesian product of two polytopes. It is worthy to stress that the proposed method does not need to construct any Lyapunov–Krasovskii functional, and it can be easily realized. The effectiveness of the obtained theoretical results is illustrated by a numerical example.

Network Modeling and Control of Dynamic Disease Pathways, Review and Perspectives

“…Zhang et al [198] proposed a guaranteed cost control for a class of gene regulatory networks with multiple time-varying discrete delays and multiple constant distributed delays on the mRNA and protein concentrations such that the concentrations can be restricted by an upper bound of a defiened quadratic cost function. Xue et al [199] designed state-feedback controllers for a class of gene regulatory networks with multiple delays and bounded disturbances to ensure that the mRNA and protein concentrations can converge to a given region. Narayanan et al [200] proposed a hybrid impulsive and sampled-data controller to stabilize a class of delayed genetic regulatory networks with the diffusion of mRNAs and proteins assuming that the gene regulatory systems are not spatially homogeneous.…”

Network Modeling and Control of Dynamic Disease Pathways, Review and Perspectives

“…Zhang et al [198] proposed a guaranteed cost control for a class of gene regulatory networks with multiple time-varying discrete delays and multiple constant distributed delays on the mRNA and protein concentrations such that the concentrations can be restricted by an upper bound of a defiened quadratic cost function. Xue et al [199] designed state-feedback controllers for a class of gene regulatory networks with multiple delays and bounded disturbances to ensure that the mRNA and protein concentrations can converge to a given region. Narayanan et al [200] proposed a hybrid impulsive and sampled-data controller to stabilize a class of delayed genetic regulatory networks with the diffusion of mRNAs and proteins assuming that the gene regulatory systems are not spatially homogeneous.…”