State bounding for discrete-time switched genetic regulatory networks with time delay and exogenous disturbances.

Abstract

This article tackles the challenge of state bounding estimation for discrete-time switched genetic regulatory networks (DSGRNs) under constraints involving time delays and bounded exogenous disturbances. By introducing specific assumptions regarding system parameters, a polytope is formulated, ensuring that all solutions of the considered DSGRNs exhibit exponential convergence towards this polytope through an average dwell time (ADT) method and mathematical induction. Furthermore, particular attention is given to additional beneficial results, such as those arising in special cases, notably when the disturbances are absent (i.e., the disturbances vanish) and when initial conditions are set to zero. In the scenario of zero disturbances, a sufficient condition is established to ensure the global exponential stability of the system. Regarding zero initial conditions, a polytope is introduced to confine all system trajectories within bounds. By leveraging special properties of Metzler matrices and nonnegative matrices, we derive more succinct criteria for state bounding. Subsequently, two numerical simulations are conducted to validate the theoretical findings. Unlike existing literature, our study focuses on DSGRNs with a more generalized structure, and our employment of the ADT approach circumvents the need for complex matrix inequality computations typically found in the Lyapunov functional method.